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.
Homework Statement
A 1.8 m tall student is trying to escape from the minimum security prison in To no.
She runs in a straight line towards the prison wall at a speed of 4.0 m/s. The guards
shine a spotlight on the prisoner as she begins to run. The spotlight is located on
the ground 30 m...
Homework Statement
A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangkok to Tokyo?
Homework Equations
Distance=(speed)(time)...
Homework Statement
A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank covers $10 per square meter for the base and $5 per square meter for the sides, what...
Homework Statement
6x^2-6xy+14y^2-45=0
Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record...
Word problem Derivative of Distance formula... Super hard. Please help.
Homework Statement
A point P is moving along the cruve whose equation is y=√x. Suppose that x is increasing
at the rate of 40 units/s when x=3. How fast is the distance between p and the point (2,0) changing\
at that...
Homework Statement
Homework Equations
The Attempt at a Solution
The part I don't understand is what would be substituted (if anything) for the 24s? How will that be implemented to solve for the periods of time?
Average Rate of Change Word Problem Help!?
12. A ball is thrown vertically upward from a roof of a school that is 20 m high. The equation which gives its height above ground, in metres, after t seconds, is h(t) = - 4.9t2 + 3t + 20,
a) Calculate the average rate of change of the ball between...
Homework Statement
A searchlight is rotating from a point 'P' positioned 50m from the prison walls. The rotation of the light is represented by the equation d = 50sec2pi(t), where d is the distance in meters, from the light to the wall, and 't' is time in minutes.
a) graph the the path...
Homework Statement
A pedulum, which is 0.5 m long, swings back and forth. The angle of it's displacement from it's original position is modeled by:
Theta = 1/4Sin(Pi/3)
IN the first 4 seconds, when will the vertical displacement of the pendulum be 1 cm?
The Attempt at a Solution
What I...
Homework Statement
Sorry for the long intro:
An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz.
If air resistance is ingored, the distance, R, traveled by...
Homework Statement
Ok, the problem is you have a 30cm wire, you cut it in two and you make one into a square. The second part is a rectangle with a 2:1 side ratio. I need to find the perimeter of each of the two shapes if the outcome sum of areas were to be a minimum.
The Attempt at a...
Homework Statement
A pool in the shape of a rectangle is ten (10) m wide and twenty five (25) m long. The depth of the pool water x meters from the shallow part/end of the pool is 1 + (x^2)/175 meters.
Write a definite integral that yields the volume of water in the rectangular pool...
Homework Statement
One side of a triangle is increasing at a rate of 3cm/s and a second side is decreasing at a rate of 2cm/s. If the area of the triangle remain constant, at what rate does the angle between the sides change when the first side is 20cm long and the second side is 30cm, and...
Homework Statement
Radio direction finders are set up at points A and B, 8.68 mi apart on an east-west line. From A it is found that the bearing of a signal from a transmitter is N54.3*E, while from B it is N35.7*W. Find the distance from B, to the nearest hundredth of a mile.
A person...
Homework Statement
The image can be seen at:
http://s1130.photobucket.com/albums/m521/harrietstowe/?action=view¤t=photo1.jpg
The rectangle in the picture represents the floor of a room and AB a straight piece of string lying on the floor whose ends touch the opposite walls w1 and w2...
Hey everybody, I need help on a few word problems. The major problem I'm having is finding a formula to use.
A bus is going to a football game and leaves at 4:00pm. It travels 20.91 miles to the game in 33 minutes. What is the bus' average speed in miles per hour?
I'm completely clueless...
Homework Statement
A pond initially contains 1,000,000 gal of water and an unknown amount
of an undesirable chemical. Water containing 0.01 gram of this chemical per
gallon flows into the pond at a rate of 300 gal/hour. The mixture flows out at
the same rate, so the amount of water in the...
In order to be included on the ballot in a certain city, a candidate must get at least 12.5% of the registered voters in each of three or more of the city's five districts to sign a petition. The ratio of the numbers of registered voters in the five districts is 6:5:5:4:5. In order for a...
Homework Statement
Miguel Tijera plans to rent one house and purchase another. He estimates that mortgage interest deductions on his federal income tax will be 25% of his mortgage payments. He wants to spend no more than $800 a month on rent and $2000 a month on rent and mortgage payments...
Homework Statement
Consider a projectile launched at a height of h feet above the ground at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modled by the parametric equations
x=(v[SUB]0cos θ)t and y=h + (v[SUB]0 sin θ)t-16t2.
The...
Homework Statement
The orbits of Earth and Venus are so close to being circles that on the scale of the diagram below, you would not be able to tell they were not circles.
a) Do you think the assumption that the orbits are circles has a significant effect on the result?
b) Where in the...
In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then
h(t) = 125sin (pi/25t - pi/2) + 125
represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds...
Homework Statement
On the first day, shoes in a shop were sold for $30 each. On the second day, the price of a shoe was reduced and the number of shoes sold on the second day increased by 50% while the money collected increased by 25%. Find the price of a shoe sold on the second day. The...
Homework Statement
When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance r away from q, the acceleration of q is
a. in the direction of the charge Q1 or Q2 of smaller magnitude.
b. in the direction of the charge Q1 or Q2 of greater magnitude...
Homework Statement
A swimming pool is 20 feet wide, 40 feet long, 3 feet deep at the shallow end and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8 feet^3/min, how fast is the water level rising when the depth at the deepest point is 5 feet?
Homework Equations...
Homework Statement
A Parabolic archway is 12 meters high at the vertex, at a height of 10 meters, the width of the archway is 8 meters. How wide is the archway at ground level?
Homework Equations
given in the picture it has (-4,10) and (4,10) along with vertex (0 ,12)
The Attempt at...
Homework Statement
Jake is 1 mile per hour faster on his skateboard than Tom. Both skate 24 miles one day from the park to the mall. Tom took 2 hours longer than Jake. What was Tom's average speed?
Homework Equations
d=rt
The Attempt at a Solution
So I set up a table w/ d=24, rate...
Homework Statement
As long as N isn't too small, the growth of cancerous tumors can be modeled by the Gompertz equation,
dN/dt=-rN*ln(N/K),
where N(t) is proportional to the number of cells in the tumor, and r, K > 0 are parameters.
(a) Sketch the graph f(N)=-rn*ln(N/k) verses N...
Homework Statement
( URL of image in case it doesn't display : http://imgur.com/wrzYH.png )
The axes x and y are measured in miles.
In the figure, the LORAN stations at A and B are 520 mi apart, and the ship at P receives station A's signal 2,640 microseconds (ms) before it receives the...
Homework Statement
A gallon of milk will last 192 hours at 0 degrees celcius, 42 hours at 22 degrees celcius, how long will it last at 30 degrees celcius?
Homework Equations
The Attempt at a Solution
Homework Statement
I need to figure out the formula and answer for this word problem.
it says "A few years ago at her birthday party, mary said take the year it will be 3 decades from now. Subtract the year of my birth and add the year it was one century ago. You now have my birth year...
Homework Statement
When a cake is removed from an oven, its temperature is measured at 300 degrees F, 3 min later its 200, how long will it take for it to cool off to 75? room temp is 70. Assume Newtons law of cooling applies. The rate of cooling is proportional to the difference between the...
An object having mass 70kg falls from rest under the influence of gravity. The terminal velocity of the object is -20 m/s. Assume that air resistance is proportional to velocity.
Q) Find the velocity and distance traveled at the end of 2 seconds.
I got an answer for the velocity, but I am...
Water is run at a constant rate of 1 ft^3/min to fill a cylindrical tank of radius 3ft and height 5ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by...
Homework Statement
The statue of libery is 46 meters tall and stands on a plinth 47 meters tall.
How far back should a 2m tall person stand back to obtain the largest viewing angle? There is 66m of land in front of the statue, will the position be within these 66 meters?
Homework...
Homework Statement
I just translated this word problem:
The zone of a alga increases every 2 month about the factor 4. How many days does the alga needs to increse into the double? How many days ago has the alga been the half?
Homework Equations
The Attempt at a Solution...
Homework Statement
A satellite is deployed from a space shuttle into an orbit which goes alternately north and south
of the equator. Its distance from the equator over time can be approximated by a sine wave. It
reaches 4500 km, its farthest point north of the equator, 15 minutes after the...
Urgent First-Year Calculus Word Problem! Help needed ASAP!
Homework Statement
Hey this is a first year calculus word problem:
A third design question involves our plan to provide interested tourists with a video of themselves on our biggest Ferris wheel. The idea is to place a camera on...
Homework Statement
Here the the word problem:
Genelle and Eljen can paint a room together in 4 hours. Working alone, Genelle can paint the room in two hours less than Eljen can. Find how long it takes Eljen to paint the room alone.
Homework Equations
Maybe, this problem can be solved using...
Homework Statement
The leaning tower of Pisa was originally perpendicular to the ground and 179ft tall. Because of sinking into the earth, it now leans at a certain angle 'theta' from the perpendicular, as shown in the figure. When the top of the tower is viewed from a point 150ft from teh...
Please. Need help with quadratic word problem!
PLEASE HELP WITH THIS!
An object is launched upward at 9.8 meters per second (m/s) from a 39.2-meter tall platform.
a)write an equation representing this path
b) What is the height of the object after 3 seconds
c) For what time span is the...
Homework Statement
A cylindrical can is to hold 4π cubic units of juice. The cost per square unit of constructing the metal top and the bottom is twice the cost of constructing the cardboard side. what are the dimensions of least expensive can?
calculus must be used logically to solve this...
Homework Statement
A 5 pound mixture of barley and oats is 4/5 oats by weight.
How much barley in pounds must be added to the mixture to make it 3/5 oats by weight?Homework Equations
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The Attempt at a Solution
I honestly cannot figure this problem out. The book gives the answer and...
Homework Statement
A manufacturer produces DVD at $2 per each unit. The selling price is $5 each. 4000 units are soled per month. The manufacturer want to raise the price and estimates that for each $0.50 increases in price, 200 fewer DVDs will be sold each month.
Relationship between DVD...
Homework Statement
Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t).
Express dV/dt in terms of dr/dt.
2. The attempt at a solution
Volume of a Sphere = 4/3 pi r3
I took the derivative of the formula...
the pathway for a mineshaft is described as follows: The first shaft extends north and down at an angle of 3.5 degree for 225ft to a vertical shaft which 125ft long. A third shaft then extends north and down at an angle 6.8 degree for 175ft. What is the total depth below ground level at the end...
Homework Statement
(a) Use a graphing calculator or computer to fit an exponential function to the data. Graph the data points and the exponential model. How good is the fit?
(b) Estimate the rates of population growth in 1800 and 1850 by averaging slopes of secant lines.
(c) Use the...
Homework Statement
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 54 m.
Homework Equations
dy=dy/dx *dx
Surface area of a hemishpere=2pi*r^2
The Attempt at a Solution
dy=4pi*r dx
dy=4pi*27...
Homework Statement
You are traveling at 20 m/s and the stop light turns yellow. You have to make an insantaneous decision: Do i brake before the intersection or do I hit the gas pedal and beat the light? Keep in mind that this particular intersection is photo-enforced, and an $85 traffic...
Fencing around a rectangular parking lot costs twice as much along the side facing the street than the other three sides. The fencing along the back of the lot costs $10 per meter. Express the cost C of the fence as a function of the width w if the length of the street side of the parking lot is...