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.
So far for the word problem I have: A 100 g particle, traveling at 40 m/s, collides inelastically with another 100g particle traveling towards it at 30 m/s.
Now from the equation provided we need the question to ask us to find delta t, and that's simple enough but I'm not sure what that 1/2 is...
I have great difficulty understanding the solution. I'll go through it line by line:
c boys can mow a acres in b days. This condition is from the problem and I understand it.
1 boy can mow a acres in bc days. Why not b/c days? After all isn't 1 boy from c/c=1?
n boys, or 1 man, can mow a...
Proof: Let x be the number of men, y be the number of women
and z be the number of children.
We need to find the solutions in the non-negative integers
for the Diophantine equation 3x+2y+0.5z=100 such that
x+y+z=100...
Proof: Let x be the number of dollars and y be the number of cents in the check.
Then we have 100y+x-68=2(100x+y).
From the hint, we get the following Diophantine equation: -199x+98y=68.
Applying the Euclidean Algorithm produces...
This is an extended thinking portion in my textbook, and I would really like to know why this is. I'm not too sure what the answer to this is, and unfortunately, there is no answer to extended thinking in my textbook. I've been trying to figure this out for some time now and I'm completely stumped.
Summary:: I have a document which was written by previous tutor supervisor/instructor at my undergraduate school. I want to learn how to use this technique for other math/physics subject besides algebra... I will provide an example of how to use this technique. I found an old textbook (College...
The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.
I never saw an age problem involving a ratio but let's see.
Abraham to Adam = 5 : 7
Let x = present age of Abraham and Adam.
Age of Abraham = 5x...
Hello! I am having trouble with this question. Please look at the image. I understand that I’m supposed to use the A = p *(1 + r/n) [(1 + r/n)n*y - 1] / (r/n) formula but I’m really stuck on this problem.
The sketch:
First of all find the length of PQ on i.e
$$4 \ inches - 1 \ mile$$
$$1.2 \ inches - x \ mile$$
$$x = \frac{1.2}{4} = 0.3 \ mile = 1584 \ ft$$
Now, I do not understand where shall I draw the horizontal, and the connection between the lengths of the contours, so I'll be grateful if...
Hello, I don't know anything about cricket, so I'll be grateful if you help me with constructing a diagram for this problem.
Here's my attempt.
I looked up on the internet and I pretty much get the idea of pitches and wickets, but still cannot connect everything together.
Thank you.
Hello!
I'm trying to solve this problem.
Here's the diagram I tried to make.
I have difficulty understanding this math problem.. I've tried to solve the problem using the symmetry of the triangles but I didn't get the right answer, and I can't seem to understand the "concept" of the horizon...
I have this word problem that is asking for two different answers, the equation for the data and to calculate the shipping rate. I'm not understanding how to address either of the questions. Will someone please help me with this answer?
This seems like a simple problem, but I am a little confused by a few things.
For one, what is the use of the piece of information that when they charged $100 per person they got 3000 people to come?
Also, how should I proceed with the information "for every $2 decrease in price they would have...
I was able to do the first graph knowing that acceleration is 9.8 and my distance goes up by 10s (y-axis) and my time goes up by 1s (x-axis). For the other 3 graphs, I'm not sure where to begin because I don't know how to figure out my velocity
In an inter school basketball league, the team from Brent International School has won 12 out of 25 games, a winning percentage of 48%. We have seen that they need to win 89 games consecutively to raise their percentage to at least 60% . What will be their winning percentage if they win;
a. 10...
I am studying to take a real estate exam. I am having problems determining the correct formula on the percentage problems. I need help solving the answer and understanding the correct formula. Help is much appreciated. The math problem is:
The subject is a mixed use undeveloped property with 3...
Help me solve this word problem please & explain how you did it-thanks so much, I 'm tearing my hair out.
Jason purchased a can of tomato sauce and three pounds of apples for $\$7.05$. Gina purchased a can of tomato sauce and 5 pounds of apples for $\$11.35$. What is the price of the tomato...
The problem as given in the book:
The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price?
All I could think was trying to work...
George makes a paper boat with his brother Bill and goes out in the rain to play with it. It falls in the stream along the curb, racing towards the sewer.
Let t be measured in seconds, p be the velocity of the paper boat in meters/second and g be George’s velocity, measured in meters/seconds...
2. Betty would like your help planning her garden whose rows are all of equal length. She would like to grow carrots, beans, sunflowers, tomatoes and peppers. She tells you she would like to devote twice as many rows to growing peppers as she does to beans. She only has enough tomato plants to...
The 100W light bulb (cost 0.60 dollars) is not going to be used anymore and is being replaced with the 20W (cost 3 dollars) low energy light bulb.
If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly...
So I have this word problem as seen below:
Joy and Ethan have agreed to meet for dinner between 8:00 PM and 9:00 PM. Suppose that Ethan may
arrive at any time between the set meeting. Joy on the other hand will arrive at the set meeting under the
following conditions:
• Joy will always arrive...
The question is as follows :
''Given that January 1st, 2018 is a Saturday, write an algorithm to determine the day of the week for a given date provided as an input. The input to the algorithm should be in the format YYYYMMDD, where March 21st 2018 is written as 20180321''
My issue is as...
The question asks, "A one-way road has an overpass in the form of a semi-ellipse, 15 ft high at the center, and 40 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass?"
I don't think this is a super complicated question yet it proves to be too...
March bill was \$400.00 for 25% to be paid of that. There is a recurring overpayment amount of \$85.00 so \$85.00 was to be withdrawn from the 25% of \$400.00 for a total of \$15.00.
\$400.00 x .25 = \$100.00
\$100.00 - \$85.00 = \$15.00
However, rather than doing that; the following was...
So I was just wondering if someone could check my method for (b) as sometimes I can have a tendency of getting the relative components wrong ect.
Diagram 1
(a)
Time for PY: ##T=L/c##
Time for YP: ##T=L/c##
Total Time:##2L/c##
(b)
Velocity for PY: ##c-v##...
So I am a bit stuck on this question as my result using the above equations dose not give an numerical value which I assume from the question is needed.
So here my method for solving
My first thought was that if on the planet the person can throw a rock 10 time further then that it implies in...
I have a word equation i cannot figure out! anyone have any ideas?
There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the...
A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ?
My attempt:
(30/4)/1=(40/x)/1
(30 persons per 4 days per task=40 persons per x days per task)
Doing this way i found x= 5.33 day or 5 whole days .
is this correct way of doing this problem?
Problem: Dr. L and his cat Kepler are coming home from fishing. They ended their trip on the south bank of a river, directly across a 1200 m wide river, from where Caroline was going to pick them up on the north bank. They are in identical boats that can travel at 4 m/s (Vb). The river is...
Homework Statement
During a heavy rain, a section of mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40km x 0.40km and that...
So I am very, very new to logic based questions, and in the past have solved some with relative ease but whilest scrolling through the next to find some example stuff I came across a website that gives a question and hints to the question if stuck, so I thought this would be good practice. But...
At a post office, there are three parcels of different masses. The mass of the first parcel is y grams. The mass of the second parcel is 500 grams greater than that of the first parcel. The third parcel is 210 grams lighter than the first parcel.
a) Find the total mass, in grams, of the three...
John is x years old and his mother is 25 years older than he is.
a) How old is John's mother?
My answer: x + 25 = mother
b) What is the sum of their ages now?
my answer: x + mother = current age
c) when john is 12 years old, how old is his mother?
my answer: 12 + 25 = 37.
Homework Statement
If a father is twice as old as his son. six years ago father was thrice as old as his son. Find the percentage.
A.10
B.12
C.120
D.6
Homework Equations
The Attempt at a Solution
first i am trying to express the equation
f=age of father
s=age of son
f=2s (father is twice as...
Homework Statement
A canoe is floating down a creek. The canoe is first spotted 80 feet away. 7 minutes later the canoe is 45 feet away, making a 40° angle between the two sightings.
How far did the canoe travel?
Homework Equations
Law of Sines and Law of Cosines
The Attempt at a Solution...
An airplane is flying on a bearing of South 27degrees West at 485 mph. A 35 mph wind is blowing from a direction of South 72degrees East. What is the actual bearing of the plane and the ground speed of the plane? I've been stuck on this problem for so long and am going to ask for help
Homework Statement
Is it possible to accurately approximate the speed of a passing car while standing in the
protected front hall of the school?
Task: Determine how fast cars are passing the front of the school. You may only go
outside to measure the distance from where you are standing to the...
1. Homework Statement
You’re testing the effect of a noxious substance on bacteria. Every 10 minutes, one-tenth of the bacteria which are still alive are killed. If the population of bacteria starts with 10^6, within which period of 10 minutes will 70% of the bacteria be killed?
Homework...
Homework Statement
You should shoot a basketball at the angle ##\theta## requiring minimum speed. Avoid line drives and rainbows. Shooting from (0, 0) with the basket at (a, b), minimize ##f(\theta)= 1/(a \sin (\theta) \cos (\theta) -b \cos^2 (\theta))##.
(a) If b =0 you are level with the...
Homework Statement
Find the 2 unknown variables.[/B]
Homework Equations
Am I doing this right? Can someone help me find the solution?[/B]
The Attempt at a Solution
To compute for the velocity of the target/arrow combination immediately after the collision...
I have this word problem, and was wondering how I would go about creating a system of equations.
Here is the question:
Problem: You are a small forest landowner, and decide you want to sustainably harvest some of timber on your property. There are costs related to the infrastructure needed to...
So I have an investment word problem that I have tried multiple times and have not been able to get the right answer.
"If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives is 4.5% of the total...
Homework Statement
A friend tells you that she is planning to change her life by moving from the UK to the Brazilian resort of Guarapari, where she intends to make and sell food on the beach for the tourists for 8 hours a day, every day. Whilst pleased for her adventurous plan, you are a little...
Homework Statement
A person lost 10% when he sold goods at Rs 153 for how much should he sell them to gain 20% .
Homework Equations
The Attempt at a Solution
0.10(153)= 15.3
153+15.3= 168.3 ( the price of product for no profit)
0.2(168.3)=33.6
(168.3+33.6)= 201.9 rupees is the 20% gain ...
Homework Statement
A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?
Homework Equations
The Attempt at a Solution
I just imagined walls and paiting work and try to assign them
and i found that it tooks 55 days working...
Homework Statement
You have an outstanding student loan with required payments of $500 per month for
the next four years. The interest rate on the loan is 9% APR (monthly). You are
considering making an extra payment of $100 today (i.e., you will pay an extra $100
that you are not required to...
Homework Statement
Suppose that b is 20% more than a, c is 25% more than b, and d is k% less than c. Find k such that a=d
Homework Equations
a=d; b=1.2a; c=1.25b=1.5a
The Attempt at a Solution
1. a=##\frac{c}{15 }##=d=##\frac{100c-k}{100}##
2. By multiplication of extremes and means we...
Homework Statement [/B]
Please check the attachments as to view the questions.
Homework Equations
Ek= 1/2 mv^2
EPSpring= 1/2 kx^2
The Attempt at a Solution
A) EPSpring= 1/2 kx^2
1/2 (100)(0.11) ^2
=0.605 J
B) Is ok I understand it.
C)
EKO=EKF
EPSpring(Initial) + EK(Initial) =...