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.
Tod injured his wrist while he was skateboarding. To relive the pain his doctor prescribed him some medication. He takes 500mg of medicine every 6h. Only 25 % of the medication remains in his body by the time he is ready to take another pill.
Write and equation to model this.
so 25% is...
In a motorcycle race, one lap of the course is 650m. At the start of the race, Genna sets off 4 seconds after Tom does, but she drives her motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than he does.
a) Find the speed at which each of them is driving.
b) Find the tim etaken...
"An object moves so that its velocity, v is related to its position. s according to v = (b^2 + 2gs) ^1/2 where b and g are constants. Show that the acceleration of the object is constant."
I typed out the question exactly as it is. I'm confused because I don't really get what to do. To show...
Hello,
This is what am trying to solve
A balloon is rising at the rate of 5ft/s. A boy is cycling along a straight road at a speed of 15ft/s.when he passes under the balloon it is 45 ft above him.
How fast is the distance between the balloon and the boy increasing 3 seconds later...
Question: A spherical bubble of radius 1 is surmounted by a smaller, hemispherical bubble, which in turn is surmounted by a still smaller hemispherical bubble, and so forth, until n chambers including the initial sphere are formed. What is the maximum height of any bubble tower with n chambers...
"A plane is observed approaching your home and you assume its speed is 550 miles per hour...The angle of elevation of the plane is 16 degrees at one time and 57 degrees one minute later. Approximate the altitude of the plane."
Ok I tried drawing triangles for this but I keep getting to a...
Having trouble with this problem.
"The mean distance from the sun to Mars is 141.7 million miles. If the eccentricity of the orbit of Mars is .093, determine the maximum distance that Mars orbits from the sun."
So basically what it is asking for is half the length of the major axis right...
Would anyone happen to know why I can't highlight a chunk of writing in Microsoft Word and then hit the backspace button to delete it? I press it but nothing happens so I now have to use the delete button which is odd...not used to it.:rofl:
The backspace button will work if I simply place...
I encountered yet another difficult one but this time, this problems a bit funny because there's 2 different cases that need to be put into consideration and I don't know exactly how to approach this question.
It goes like this:
"A Pedestrian is running at her maximum speed of 6.0m/s to catch...
Suppose that in any given year, the population of a certain endangered species is reduced by 25%. If the population is now 7500, in how many years will the population be 4000?
Well, I know that the formula for this is P(t) = Cekt.
I just can't figure out the value of k.
i did 7500 x .25 =...
I'm not sure if this is calculus, but it is like a review in my calculus class.
Suppose that in any given year, the population of a certain endangered species is reduced by 25%. If the population is now 7500, in how many years will the population be 4000?
I've known how to do this before...
hi,
Someone please help me with this problem.
How many meals were served per labor minute if 34 FTF produced 3800 meals in one 40 hour week, thanks. I don't know where to begin.
I can't seem to figure out this problem.
Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10.
I start by drawing the diagram and it seems to me like the circle radius corresponds with a line from the center of the rectangle to one of the...
One question says "It has been said that centripetal force is is not a unique force. Outline what a centripetal force is as well as three (explained) examples of what is meant by this statement.(5 marks)" Here is my theory:
Newtons first law states that an object in motion stays in motion...
i don't know if one could do this without the diagram but...
a rain gutter is to be made of aluminum sheets that r 12 inches wide by turning the edges 90 degrees. what depth would provide maximum cross-sectional area and hence allow the most water to flow?
Question: A rectangle with a perimeter of 40cm is rotated around one of its sides, creating a right cylinder. What is the largest possible volume for this cylinder?
Here's what I have done so far:
Equation #1:
40 = 2h + 2r
r = 20 - h
Equation #2:
Volume = pi*r^2h
= pi(20-h)(h)
= 20pi*h...
A baseball is thrown at an angle of 24 degrees relative to the ground at a speed of 29.3 m/s. The ball is caught 65.0 m from the thrower. The acceleration of gravity is 9.81 m/s^2.
a) How long is it in the air? Answer in units of s.
b) How high is the tallest spot in the ball's path...
Alright, First I'll explain the problem, then I'll explain what I've tried and what's confusing me.
A 45.0 kg girl is standing on a 150 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank...
Tricky word problem.
Hi I'm having trouble figuring out how to approach this word problem and wonder if anyone had tips.
Problem:
Just suppose, for the sake of argument, that you have a large block of stone. While staring at this block of stone, it dawns on you that perhaps you should...
chem word problem ! please help
Hi ,
This is a Hw question i have am stuck on i don't know how to solve it ...
A pharmacist is to prepare 16 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 10%...
Word problem !
Hi ,
This is a Hw question i have am stuck on i don't know how to solve it ...
A pharmacist is to prepare 16 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 10% solution and 1%...
Hello All
I have this word problem that I am having problems with
Here it is
A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area in^2. What are dimensions of the rectangle??
Here is what I have figured out. Not sure if it...
1. A nurse must make sure that a patient receives at least 30 units of a certain drug each day. This drug comes from red pills or yellow pills, each of which provides 3 units of the drug. The patient must have twice as many red pills as yellow pills. At least how many yellow pills will satisfy...
1. A tank holds 90 L of chemical solution. Currently the solution has a strength of 20%. How much of this should be drained and replaced with an 80% solution to have a final strength of 30%?
Hello I have this word problem that I am having problems solving. Hopefully someone can help
Here is it.
A piece of wire 10m long is cut into two pieces. On piece, of length x, is bent into the shape of a square. The other is bent into the shape of a equilateral triangle.
(a) expess...
A club consisting of seniors and juniors has 15 members. After seven more seniors and three more juniors join the club, the ratio of juniors to seniors is 2:3. How many juniors are in the club?
I guess the thing that screws me up is the ratio part. I don't know what to do. I've found a...
Hello, I have been stuck on this problem for about a week and a half. I was wondering if there was anyone out there who might understand it and explain it clearly to me.
Suppose a volume of 1000 drops of water contains 2000 bacteria, separate from each other and thoroughly mixed in the...
Hi,
This is the problem:
Lorraine has $7.70 in dimes and quarters. If the number of quarters is two more than twice the number of dimes, how many of each type does she have?
I know the answer is 12 dimes and 26 quarters by figuring it in my head, but my professor requires us to show work to...
Hi, I've done most of my homework, but can't figure this one out. If anyone could explain what to do, I would really appreciate it.
*i got 78 for an answer, but its wrong*
It is exactly noon. The hour hand of a clock is 8cm long. If the top of the clock is 50 cm from the ceiling and the...
An electron starts from rest 72.5 cm from a fixed point charge with Q=-0.125µC. How fast will the electron be moving when it is very far away?
The answer the book says is 2.33 x 10^7 m/s, but I don't know how they got that answer.
The equation I think I need to use is V=k(Q/R)
So I...
An appliance store sells only two brands of refigerator. The ratio of the number of brand X refigerators sold at this store to the number of Brand Y refigerators sold is about 4 to 11. Of the next 100 refigerators the store sells, approximately how many will be brand Y?
I don't know how to...
http://www26.brinkster.com/nick898/question.htm
I`ve scanned the question so you can understand it better. This is how
I started...
x+1/x - 1/4 = x+3/x+2
But this is how far I got. I don`t know what do after this part and I
don`t even know if what I`m doing is correct.
In my algebra textbook the following problem is given:
Ken and Bettina Wikendt live in Minneapolis, Minn. Following a severe snowstorm, Ken and Bettina must Clear the driveway and sidewalk. Ken can clear the snow by himself in 4 hours. Bettina can clear the snow by herself in 6 hours. After...
Bill Bored is out to get his kicks. He starts playing Russian roulette with a 3.25 kg shot put. He takes his chances throwing the ball straight up into the air and waiting to see if the ball hits him in the head on its way down. Bill is 1.95 m tall and the ball rises 4.0 m above the point of...
Jane, looking for Tarzan, is running at top speed (5.6 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward?
I know the answer is 1.6 m, but I don't understand how to get it.
In class, we have been using the equation: 1/2mv^2 + mgy =...
For security, a credit card number is coded in the following way, so that it can be sent as a message. "Subtract each digit from 9"
code the credit card number 3201 2342 3458 0931
I don't understand the subtract each digit from 9 is that to code or uncode? Also for the above code the...
Bob and Jack enter a 1000 km bike race. Bob cycles 4 km/h faster than Jack, but his bike gets a flat tire, which takes 30 minutes to repair. If the both of them finish the race in a tie, then how fast was each boy cycling?
Wooooh I have no clue as to how to solve this problem, can someone...
I hope that I construct this problem correctly. I am trying to...um, help a friend fight a speeding ticket. Thanks in advance for any help.
The posted speed limit was 25 MPH. The officer was stopped at an intersection as I passed by him on the perpendicular and "estimated" that Iwas traveling...
I'm having problems setting up this problem (word problems are my worst downfall!)
a rectangular container with an open top is to have a volume of 10 meters cubed. The length of its base is 2x the width.
The cost of the base is $12 per sq meter. The cost of the sides is $5 per sq meter. find...
Hey,
I'm having some problems with some Fraction Word Problems in Algebra, can anyone assist me as to how I'm supposed to create my equations from the following two word problems in order to solve?
Thanks:
1) A 150mL solution of alcohol in water is 75% alcohol. How many mL of a 67% solution...
A certain manufacturing plant burns fossil fuel in its manufacturing process. The fuel that is obtains can be divided into 3 types - low emmission fuel, moderate emmission fuel and high emmission fuel. Federal law requires that high emmission fuel be discarded and that the company can burn at...
A man is standing at a launch site. The rocket doesn't liftoff. Frustrated s/he throws it straight up with a speed of 12.42 m/s. It is caught on the way down at a point 5.0 meters above where it was thrown, by a fellow rocketeer on the second floor, who doesn't want to see any harm come ot this...
A car is traveling along a road at 35.1 meters/second(m/s). All of a sudden the navigator yells "Stop! The driver quickly applies the brakes at an acceleration of -2m/s/s (meters per second squared) and comes to a stop.
How much distance it take to stop the vehicle?
My question is what...
A can do a piece of work in 4 days and B in 6 days. How long will they require working together ?
Hint. 1/4 + 1/6 = 1/x
I just don't get them :redface: ( The problem and the hint).
Can you help me understand it ?
Having some trouble with this. Would appreciate your help please.
An object weighing 128 pounds is suspended from a spring, streching the spring 2 feet beyond its natural length. The object is then released from rest at a point 6 inches above the equilibrium position.
a. Find a function...
Hi,
Ok I'm havin troubles trying to solve this calculus problem.
-Rolling a Ball Bearing-
A ball bearing is placed on an incline plane and begins to roll. The angle of elevation of the plane is θ.
The distance (in meters) the ball bearing rolls in t seconds is
s(t) = 4.9(sin...
Need help on this word problem please. I don't even know where to start with this one.
If you convert 3 kg of ice at -30 degrees C into 3 kg of steam at 120 degrees C. Using this as a model can you explain how we make ice-cream with ingredients of 5 degrees C into soft ice-cream at...
I missed the test question can anyone explain what they did to solve for this.
In grinding a steel knife blade(SH=.11 cal/g*C) the metal can get as hot as 400C. If the blade has a mass of 80g, what is the minimum amount of water needed at 20C if the water is not to rise above the boiling...
A certain dog whistle operates at 23,5khz, while another brandX operates at an unknown frequency. If neither whistle can be heard by humans when played seperately but a shrill whine of frequency 5kHz occurs when they are play simultaneously, estimate the operating frequency of brand X...