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Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen/Homework 13

2011-02-04T02:04:40Z

MatthewRobinson:

Homework 13 Group Work

The Logarithmic Scale and How it is applied to the Richter Scale

The logarithmic scale is used generally when there is a very wide range of values. It is important to note that the change of a specific value on according to a logarithmic scale does not depend on "the size of the change is proportion to the value of it self"(http://mathforum.org/library/drmath/view/55574.html) This can be explained easier if one looks at the difference between a linear and logarithmic scale. A linear scale is used "if adding 1 to a value is just a big as a change whether the original value was 1 or 1000"(http://mathforum.org/library/drmath/view/55574.html). In other words a linear scale is used when one can see on a graph the difference of an increase in 1(or any reasonably small number)

GRAPH OF LINEAR EQUATION

http://en.labs.wikimedia.org/wiki/Algebra/Function_Graphing

A logarithmic scale is used when the, "doubling of a value is just as big as a change whether it is from 1 to 2, or 1000 to 2000(http://mathforum.org/library/drmath/view/55574.html). Therefore the logarithmic scale was created and along the Y-Axis the number increase exponentially by ten each increasing value.

GRAPH OF LOGARITHMIC SCALE

http://cryptodox.com/Logarithmic_scale

In summation the logarithmic scale is used when there is a large range of values, and it does so by making each increasing value tenfold of the value preceding it. The logarithmic scale is used in a few instances including the Richter Scale.

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen/Homework 13

2011-02-04T02:02:40Z

MatthewRobinson:

Homework 13 Group Work

The Logarithmic Scale and How it is applied to the Richter Scale

The logarithmic scale is used generally when there is a very wide range of values. It is important to note that the change of a specific value on according to a logarithmic scale does not depend on "the size of the change is proportion to the value of it self"(http://mathforum.org/library/drmath/view/55574.html) This can be explained easier if one looks at the difference between a linear and logarithmic scale. A linear scale is used "if adding 1 to a value is just a big as a change whether the original value was 1 or 1000"(http://mathforum.org/library/drmath/view/55574.html). In other words a linear scale is used when one can see on a graph the difference of an increase in 1(or any reasonably small number)

GRAPH OF LINEAR EQUATION

[[File:Linear Equation Pic.png]

A logarithmic scale is used when the, "doubling of a value is just as big as a change whether it is from 1 to 2, or 1000 to 2000(http://mathforum.org/library/drmath/view/55574.html). Therefore the logarithmic scale was created and along the Y-Axis the number increase exponentially by ten each increasing value.

GRAPH OF LOGARITHMIC SCALE

In summation the logarithmic scale is used when there is a large range of values, and it does so by making each increasing value tenfold of the value preceding it. The logarithmic scale is used in a few instances including the Richter Scale.

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen/Homework 13

2011-02-04T02:00:17Z

MatthewRobinson:

Homework 13 Group Work

The Logarithmic Scale and How it is applied to the Richter Scale

The logarithmic scale is used generally when there is a very wide range of values. It is important to note that the change of a specific value on according to a logarithmic scale does not depend on "the size of the change is proportion to the value of it self"(http://mathforum.org/library/drmath/view/55574.html) This can be explained easier if one looks at the difference between a linear and logarithmic scale. A linear scale is used "if adding 1 to a value is just a big as a change whether the original value was 1 or 1000"(http://mathforum.org/library/drmath/view/55574.html). In other words a linear scale is used when one can see on a graph the difference of an increase in 1(or any reasonably small number)

GRAPH OF LINEAR EQUATION

File:Y_equals_x_plus_2.PNG

A logarithmic scale is used when the, "doubling of a value is just as big as a change whether it is from 1 to 2, or 1000 to 2000(http://mathforum.org/library/drmath/view/55574.html). Therefore the logarithmic scale was created and along the Y-Axis the number increase exponentially by ten each increasing value.

GRAPH OF LOGARITHMIC SCALE

In summation the logarithmic scale is used when there is a large range of values, and it does so by making each increasing value tenfold of the value preceding it. The logarithmic scale is used in a few instances including the Richter Scale.

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen/Homework 13

2011-02-04T01:57:42Z

MatthewRobinson: Created page with "Homework 13 Group Work The Logarithmic Scale and How it is applied to the Richter Scale The logarithmic scale is used generally when there is a very wide range of values. It i..."

Homework 13 Group Work

The Logarithmic Scale and How it is applied to the Richter Scale

The logarithmic scale is used generally when there is a very wide range of values. It is important to note that the change of a specific value on according to a logarithmic scale does not depend on "the size of the change is proportion to the value of it self"(http://mathforum.org/library/drmath/view/55574.html) This can be explained easier if one looks at the difference between a linear and logarithmic scale. A linear scale is used "if adding 1 to a value is just a big as a change whether the original value was 1 or 1000"(http://mathforum.org/library/drmath/view/55574.html). In other words a linear scale is used when one can see on a graph the difference of an increase in 1(or any reasonably small number)

GRAPH OF LINEAR EQUATION

A logarithmic scale is used when the, "doubling of a value is just as big as a change whether it is from 1 to 2, or 1000 to 2000(http://mathforum.org/library/drmath/view/55574.html). Therefore the logarithmic scale was created and along the Y-Axis the number increase exponentially by ten each increasing value.

GRAPH OF LOGARITHMIC SCALE

In summation the logarithmic scale is used when there is a large range of values, and it does so by making each increasing value tenfold of the value preceding it. The logarithmic scale is used in a few instances including the Richter Scale.

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen

2011-02-04T01:44:39Z

MatthewRobinson: /* Homework */

{{
Infobox MATH110 Teams
| team name = Schaffhausen
| member 1 = Jose Torres-Torija Cubillas - Zombie
| member 2 = Kazi Ahmed - Lazy
| member 3 = Matthew Robinson - Tired
| member 4 = Trevor Shumka - Rowdy
}}
In workshop J.

=Homework=
* [[Course:MATH110/003/Teams/Schaffhausen/Homework_11|Homework 11]]
* [[Course:MATH110/003/Teams/Schaffhausen/Homework_12|Homework 12]]

* [[Course:MATH110/003/Teams/Schaffhausen/Homework_13|Homework 13]]

User:MatthewRobinson

2011-01-28T06:26:04Z

MatthewRobinson:

I'm Matt Robinson and I hope to either major in economics or political science. matt_robinson77@hotmail.com

Renes Descartes was born on March 31st 1956 in La Haye en Touraine a city in France, which would later be named Descartes in honor of “The Father of Modern Philosophy.” Descartes had a huge influence on Western Philosophy and Mathematics and was also a physicist, and writer. He is well known for his famous line in his book Discourse on the Method (1637), “I think therefore I am.” He also influenced mathematics through analytical geometry. Analytical geometry or Cartesian geometry is the study of geometry using a coordinate system and the principals of algebra. Analytical geometry is used to define geometrical shapes in a numerical way and getting numerical information from that representation. Descartes lived most of his life in the Dutch Republic and died at the age of 53 he is still a historical figure for his life work especially in mathematics and philosophy.

Calculus can be applied to many situations in life. The study of basic economics requires the basic understanding of math. Some say that calculus is the language of economics and the means of how economists solve problems. Calculus tends to heavily focus on functions and derivatives. Functions, examine the relationship of more than one variables. Economists also use X and Y to describe variables and try to understand the relationship between the two variables. Derivates explain the rate of change of one variable in accordance with the other. Calculus can be used to find marginal cost, marginal benefit, marginal profit, marginal revenue, while other types of math can be used to find profit, average total cost, revenue etc.

Examples

Total Revenue
Calculus can explain the total amount of revenue received by a company based on the number of goods sold.

Marginal Revenue
Using calculus, it is easy to see the marginal revenue of items sold. Marginal revenue is the additional revenue received for selling one additional good.

Maximizing Profits
The goal of every company is to maximize its profitability. With the use of calculus, the company can find the most efficient point of producing and selling its goods.

Equilibrium
Finding the equilibrium, or the point where supply and demand meet, is an essential part of analyzing the markets and can be easily found with the use of calculus.

Interest Rates
Interest rates for a number of things, including mortgages, loans and advances, can be easily calculated with the help of calculus

Economists tend to use straight lines in their graphs to help simplify the information or problem, but with an advanced knowledge of calculus one may be able to make a more accurate graph by not just using a linear graph but a curved graph which better represents the information it is trying to give. With a better understanding of functions this would be possible.

User:MatthewRobinson

2011-01-28T06:25:19Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:24:47Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:20:33Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:13:49Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:13:25Z

MatthewRobinson:

I'm Matt Robinson and I hope to either major in economics or political science. matt_robinson77@hotmail.com

Renes Descartes was born on March 31st 1956 in La Haye en Touraine a city in France, which would later be named Descartes in honor of “The Father of Modern Philosophy.” Descartes had a huge influence on Western Philosophy and Mathematics and was also a physicist, and writer. He is well known for his famous line in his book Discourse on the Method (1637), “I think therefore I am.” He also influenced mathematics through analytical geometry. Analytical geometry or Cartesian geometry is the study of geometry using a coordinate system and the principals of algebra. Analytical geometry is used to define geometrical shapes in a numerical way and getting numerical information from that representation. Descartes lived most of his life in the Dutch Republic and died at the age of 53 he is still a historical figure for his life work especially in mathematics and philosophy.

Calculus can be applied to many situations in life. The study of basic economics requires the basic understanding of math. Some say that calculus is the language of economics and the means of how economists solve problems. Calculus tends to heavily focus on functions and derivatives. Functions, examine the relationship of more than one variables. Economists also use X and Y to describe variables and try to understand the relationship between the two variables. Derivates explain the rate of change of one variable in accordance with the other. Calculus can be used to find marginal cost, marginal benefit, marginal profit, marginal revenue, while other types of math can be used to find profit, average total cost, revenue etc.

Examples

Total Revenue
Calculus can explain the total amount of revenue received by a company based on the number of goods sold.
Marginal Revenue
Using calculus, it is easy to see the marginal revenue of items sold. Marginal revenue is the additional revenue received for selling one additional good.
Maximizing Profits
The goal of every company is to maximize its profitability. With the use of calculus, the company can find the most efficient point of producing and selling its goods.
Equilibrium
Finding the equilibrium, or the point where supply and demand meet, is an essential part of analyzing the markets and can be easily found with the use of calculus.
Interest Rates
Interest rates for a number of things, including mortgages, loans and advances, can be easily calculated with the help of calculus.

User:MatthewRobinson

2011-01-28T06:13:05Z

MatthewRobinson:

I'm Matt Robinson and I hope to either major in economics or political science. matt_robinson77@hotmail.com

Renes Descartes was born on March 31st 1956 in La Haye en Touraine a city in France, which would later be named Descartes in honor of “The Father of Modern Philosophy.” Descartes had a huge influence on Western Philosophy and Mathematics and was also a physicist, and writer. He is well known for his famous line in his book Discourse on the Method (1637), “I think therefore I am.” He also influenced mathematics through analytical geometry. Analytical geometry or Cartesian geometry is the study of geometry using a coordinate system and the principals of algebra. Analytical geometry is used to define geometrical shapes in a numerical way and getting numerical information from that representation. Descartes lived most of his life in the Dutch Republic and died at the age of 53 he is still a historical figure for his life work especially in mathematics and philosophy.

Calculus can be applied to many situations in life. The study of basic economics requires the basic understanding of math. Some say that calculus is the language of economics and the means of how economists solve problems. Calculus tends to heavily focus on functions and derivatives. Functions, examine the relationship of more than one variables. Economists also use X and Y to describe variables and try to understand the relationship between the two variables. Derivates explain the rate of change of one variable in accordance with the other. Calculus can be used to find marginal cost, marginal benefit, marginal profit, marginal revenue, while other types of math can be used to find profit, average total cost, revenue etc.

Examples
Total Revenue
Calculus can explain the total amount of revenue received by a company based on the number of goods sold.
Marginal Revenue
Using calculus, it is easy to see the marginal revenue of items sold. Marginal revenue is the additional revenue received for selling one additional good.
Maximizing Profits
The goal of every company is to maximize its profitability. With the use of calculus, the company can find the most efficient point of producing and selling its goods.
Equilibrium
Finding the equilibrium, or the point where supply and demand meet, is an essential part of analyzing the markets and can be easily found with the use of calculus.
Interest Rates
Interest rates for a number of things, including mortgages, loans and advances, can be easily calculated with the help of calculus.

User:MatthewRobinson

2011-01-28T06:12:06Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:09:50Z

MatthewRobinson:

User:MatthewRobinson

2011-01-28T06:02:44Z

MatthewRobinson:

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen

2011-01-19T06:48:00Z

MatthewRobinson: /* Other Models */

{{
Infobox MATH110 Teams
| team name = Schaffhausen
| member 1 = Jose Torres-Torija Cubillas
| member 2 = Kazi Ahmed
| member 3 = Matthew Robinson
| member 4 = Trevor Shumka
}}
In workshop J.

='''Homework 11'''=

==Model==
The information that we have been giving states that our current production rate is 20, our current total cost is $100 and our marginal cost is $7. With this information we can create an equation.

We use 20 which stands for units of production as an X value and cost which is $100 as a Y value.

F(x)=y, F(20)=$100 we know that function to be true now to create a formula we put that into a y=mx + b format plugging in 20 for x and 100 for y, this gives us 100=20m + b, our slope being our marginal cost which is the cost to produce 1 more unit, so our new equation looks like 100= 7(20) + b after we substitute 7 in. Now we solve for b which is,

100= 7(20) + b

100 = 140+b

100-140=b

-40 = b

So our final equation for this model is, y=7x - 40 if x≥20

====Now we must find the cost to produce 150 flags using this model====

we do this by plugging in 150 into x

y=7(150) -40

y=1050- 40

y= 1010, which is the cost to produce 150 flags using the model above.

====Average cost of this model at 150 units====

At the quantity of 150 flags we get the total cost to be $1010, to find the average cost of this we must divide $1010 by 150, when we do this we get that the average cost of each flag at this point in production is 6.74 which is higher than the average cost of the production of 20 flags which was an average cost of $5 per flag. So using this trend we can see that average cost increases as you produce more.

==Other Models==
The average cost remains constant as production increases.

For the average cost to remain constant to marginal cost must also remain constant a model that exemplifies this would be C(f)=MC where MC= Marginal Cost. So, if MC=10 the formula will be C(f)=10(f). Now if flags increase by 10 products the formula will look like C(10)=10(10)=100, if it increases by C(20)=10(20)=200.
The average cost diminishes as production increases.

For the average cost to diminish as production increases the marginal cost becomes lower as the number of products increases.
The average cost increases as production increases.

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

Any other interesting properties that you can think of and create a model for. Bonus points can be obtained for very interesting ideas.

Course:MATH110/Archive/2010-2011/003/Teams/Schaffhausen

2011-01-19T06:47:37Z

MatthewRobinson:

{{
Infobox MATH110 Teams
| team name = Schaffhausen
| member 1 = Jose Torres-Torija Cubillas
| member 2 = Kazi Ahmed
| member 3 = Matthew Robinson
| member 4 = Trevor Shumka
}}
In workshop J.

='''Homework 11'''=

==Model==
The information that we have been giving states that our current production rate is 20, our current total cost is $100 and our marginal cost is $7. With this information we can create an equation.

We use 20 which stands for units of production as an X value and cost which is $100 as a Y value.

F(x)=y, F(20)=$100 we know that function to be true now to create a formula we put that into a y=mx + b format plugging in 20 for x and 100 for y, this gives us 100=20m + b, our slope being our marginal cost which is the cost to produce 1 more unit, so our new equation looks like 100= 7(20) + b after we substitute 7 in. Now we solve for b which is,

100= 7(20) + b

100 = 140+b

100-140=b

-40 = b

So our final equation for this model is, y=7x - 40 if x≥20

====Now we must find the cost to produce 150 flags using this model====

we do this by plugging in 150 into x

y=7(150) -40

y=1050- 40

y= 1010, which is the cost to produce 150 flags using the model above.

====Average cost of this model at 150 units====

At the quantity of 150 flags we get the total cost to be $1010, to find the average cost of this we must divide $1010 by 150, when we do this we get that the average cost of each flag at this point in production is 6.74 which is higher than the average cost of the production of 20 flags which was an average cost of $5 per flag. So using this trend we can see that average cost increases as you produce more.

==Other Models==
The average cost remains constant as production increases.
For the average cost to remain constant to marginal cost must also remain constant a model that exemplifies this would be C(f)=MC where MC= Marginal Cost. So, if MC=10 the formula will be C(f)=10(f). Now if flags increase by 10 products the formula will look like C(10)=10(10)=100, if it increases by C(20)=10(20)=200.
The average cost diminishes as production increases.
For the average cost to diminish as production increases the marginal cost becomes lower as the number of products increases.
The average cost increases as production increases.

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

Any other interesting properties that you can think of and create a model for. Bonus points can be obtained for very interesting ideas.

Course talk:MATH110/003/Midterms and Finals

2010-12-12T04:40:08Z

MatthewRobinson:

Hi David,
I was wondering if you could post a past exam with solutions
Thanks Matt Robinson

Are we allowed to use a calculator at the final? Or if it's not needed, which would be great news :D

[[User:BellaTory|BellaTory]]

Hi David,

I was just going through the WeBWorK homework, and was wondering if we need to know the definitions of a ''jump discontinuity'' and a ''removal discontinuity''.

Thanks!
[[User:BenJeffery|BenJeffery]]

Hi Ben,

As I mentioned in class, we don't care that much about these actual words. The core idea is that there are many different reasons a function might not be continuous at a point, that's what we want you to know and be able to discuss.

-- [[User:DavidKohler|DavidKohler]] 04:48, 20 October 2010 (UTC)

All right, cool.

I was pretty sure we wouldn't have to, and having actually asked the question just made me remember the terms anyway, but I figured it was better to check than not.

Thanks!

[[User:BenJeffery|BenJeffery]] 05:02, 20 October 2010 (UTC)

Course:MATH110/Archive/2010-2011/003/Groups/Group 06/Homework 4

2010-10-20T08:22:26Z

MatthewRobinson: /* Problem 3 */

== Problem 1 ==

Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat, Bianca owns a frog that she loves, Jaela owns a parrot which keeps calling her "darling, darling", Jun owns a snake, don't mess with him, Suzan is the name of the frog, The cat is named Jun, The name by which they call the turtle is the name of the woman whose pet is Tosh, Finally, Suzan's mother's pet is Bianca.

At first this might seem puzzling because it looks as though there are six people because Suzan's mother might be another person. How they've worded the question seems to hint that one of the 5 people who isn't Suzan is her mother.

The second way you could approach the problem would be to eliminate all of the choices with logic and narrow down the corresponding names to what type of pet Suzan's mother owns. Susan's mother could be any of these people because you don't want to assume Tosh or Jun are men.

So you could start by making a chart about which animal belongs to who.

Tosh - cat

Bianca - frog

Jaela - parrot

Jun - snake

Suzan - turtle

You can get this list easily by reading the question and eliminating all the choices of animals but the turtle, which must belong to Suzan. Now you have to figure out the names of the pets which will help you figure out who Bianca belongs to and what kind of animal she is.

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named ?

Jun - snake - named?

Suzan - turtle - named ?

The name by which they call the turtle is the same as the name of the woman whose pet is Tosh. Suzan's pet is a turtle who can't be named Bianca, Suzan, Jun or Tosh. Jaela is the only name left, so the turtle is named Jaela. Tosh's owner = name of turtle. That must mean that Jaela's pet parrot is named Tosh. So we have

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named Tosh

Jun - snake - named ?

Suzan - turtle - named Jalea

The only name missing is Bianca, Suzan's mother's pet. So Suzan's mother must be Jun who owns a pet snake named Bianca.

== Problem 2 ==

Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

--> 3 people are right handed and 2 are left, it goes to say Bahao and Dylan are right handed (if Tim and Chan use different hands one of them must be right handed); this also leaves Stewart to be left handed (only 2 people are left handed and if one of them is Tim or Chan the other must be Stewart). With 3 people being under 2m tall, Stewart and Chan being the same height must be under 2m (if Dylan and Tim are different height, one must be under 2); leaving Bahao to be over 2m (if only 2 are over and Dylan and Tim are different only one of them can be over 2m leaving Bahao). You know the centre has to be left handed and over 2m. The only person left on the chart is Tim, who has nothing to his name as of yet. Only 2 people can be over 2m and if the centre is left handed it cannot be Bahao. By elimination Dylan is excluded because he is right handed, Chan and Stewart are under 2m. Tim is the only person left you can fit the qualifications. Tim must be Left handed and over 2m.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand -
* Tim -
* Chan - - Under 2m
* Stewart - Left Hand - Under 2m

Since you know the center, who is left handed and over 2m, is Tim, you can fill out the rest of the chart.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand - Under 2m
* Tim - [[ Left Hand - Over 2m - Centre]]
* Chan - Right Hand - Under 2m
* Stewart - Left Hand - Under 2m

== Problem 3 ==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

This question is best answered by using a graph I believe, First I started by putting the players names on the top of a chart and the positions on the side and going through the list and crossing off any of the players that don't fit the qualifications.

Go through the list and cancel qualifications for example
Adam does not like the catcher---he's not the catcher
Ed's sister is engaged to the second baseman---- Ed is not the Second baseman and the second baseman is not a batchelor
going on Pascal and Charles cannot be the pitcher
Ed cannot be the outfielder
Charles Hassan and Adam are shorter than sung
Pascal and Adam are not the short stop
Ed, Pascal Jason the right fielder and the center fielder means they are batchelors making the others married I used M to indicate married and B for Batchelor in my graph
Using Height Marriage and qualifications I was able to deduct and finish this graph and the following players for each position are:

Adam: third baseman
Charles: catcher
Ed: shortstop
Hassan: pitcher
Jason: second baseman
Pacal: first baseman
Sung: left field
Mathieu: right field
Bobo: center field

http://co102w.col102.mail.live.com/att/GetAttachment.aspx?tnail=0&messageId=96be92f2-dc13-11df-8bdc-00237de49116&Aux=4|0|8CD3E377DC9AB80||0|0|0|0||&maxwidth=220&maxheight=160&size=Att[[File:IMG0022-20101019-2329.jpg]]

so the graph came out really small so it will be submitted as written work on wednesday

== Problem 4 Solution 1 ==

Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?

There are 5 days in the tournament. Each day there will be three matches being played simultaneously, with a total of three matches per day.
'No girl will be playing more than 1 girl per day, if girl A is playing girl B then girl B is playing girl A'

This problem can be solved using a grid sized 6 by 6. Along the horizontal axis, mark the days of the tournament. Along the vertical axis, mark the girls (identified by a number).

[[File:Diagram_1.jpg]]

Fill the interior of the box like this: Line up the day and the name of the girl, and in that box fill in the number of the girl that she is playing.

Start with what we know:

Day 1: Carla beats Petra

Day 2: Carla beats Janet

Day 3: Janet beats Li

Day 4: Petra beats Sandra

Day 5: Fernanda plays who? - The goal of the question.

Fill in the columns. For example, to note that Carla beat Petra on Day 1, line up Carla (row 1) and day 1 (column 2), and input into that box the number 3 (which represents Petra).

[[File:Math_2.JPG]]

Next, fill in the box further using the principle that ''each girl can only play one other girl, that each girl plays only one game per day, that if girl a is playing girl b then girl b is playing girl a''.

For example, Carla is playing Petra on day one, therefore Petra is playing Carla on day 1. Fill in the appropriate box.

[[File:Math_3.JPG]]

Next, fill in all of the boxes such that each of the 6 rows and 6 column contains each of the numbers 1-6 and therefore not more than 1 of each of the digits 1-6. This requires filling in numbers at first arbitrarily, then using logical deduction and re-editing the numbers until you have a working cube.

[[File:Math_5.JPG]]

Therefore, Fernanda will play Carla on the last day.

=Problem 4 Solution 2=

From looking at the match ups you can immediately conclude that Janet must play Petra on the fifth day because both are busy not playing the other on the first 4 days.

This leaves 6 possible matchups for the Friday’s game.
Carla v Li, Carla, v Sandra, Carla v Fernanda
Li v Sandra, Li v Fernanda
Fernanda v Sandra

From here we can see that only has to play Sandra and Fernanda and since Sandra is busy on day 4, that means Janet plays Sandra on day 1 leaving the only match for Fernanda and Li eliminating Li.

'''Now we know that Fernanda plays Carla or Sandra'''

Looking at the new results we know Li plays day 1 against Fernanda, day 2 against (Petra or Sandra), day 3 against Janet, day 4 against Carla, and day 5 against (Sandra or Petra). Petra is busy day 5 against Janet so by default Li plays Petra day 2.

'''''This leaves the only remaining match on day 2 for Fernanda and Sandra.'''''''

Answer:
'''Thus Fernanda plays Carla on day 5'''''

== Problem 5 ==

'''Question:
Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.

On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.

On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.

On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.

In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.

The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.

No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?'''

''Answer:''

[[Step 1]]: First make a list of every day Homer is on vacation.

Saturday:

Sunday:

Monday:

Tuesday:

Wednesday:

Thursday:

Friday:

Saturday (2):

Sunday (2):

[[Step 2:]] Fill in all the information given.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday:

Friday:

Saturday (2): Construction

Sunday (2): Dog

[[Step 3:]] Once the information given is filled in one can see that there are only three possible days that Homer could have slept in during his vacation. We are told that the none of the noise makers stayed quiet for three days straight. Thus based on the salesman noise on wednesday they would have to make noise friday or saturday, because we are also given the information that no noisemaker pairs made noise more then once. If the salesman made noise on the second saturday he would be paired with the construction workers for the second time. From this we can determine the salesman woke Homer up on Friday. Similarly the construction worker woke Homer up on monday which means he woke him up again on either Tuesday or Thursday (sticking with the information no noisemaker didn't make noise for three days straight). Based on this information the construction worker would then have to wake him up on Thursday, if he woke him up on Tuesday there would be a three day discrepancy.

[[Step 4:]] Fill in the remaining information found through your thought process above. When done it is easy to see the only day Homer can sleep in is tuesday.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday: Construction

Friday: Salesman

Saturday (2): Construction

Sunday (2): Dog

[[Step 5:]] Homer will be able to actually sleep in on the tuesday of his vacation.

Course:MATH110/Archive/2010-2011/003/Groups/Group 06/Homework 4

2010-10-20T06:43:09Z

MatthewRobinson: /* Problem 3 */

== Problem 1 ==

Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat, Bianca owns a frog that she loves, Jaela owns a parrot which keeps calling her "darling, darling", Jun owns a snake, don't mess with him, Suzan is the name of the frog, The cat is named Jun, The name by which they call the turtle is the name of the woman whose pet is Tosh, Finally, Suzan's mother's pet is Bianca.

At first this might seem puzzling because it looks as though there are six people because Suzan's mother might be another person. How they've worded the question seems to hint that one of the 5 people who isn't Suzan is her mother.

The second way you could approach the problem would be to eliminate all of the choices with logic and narrow down the corresponding names to what type of pet Suzan's mother owns. Susan's mother could be any of these people because you don't want to assume Tosh or Jun are men.

So you could start by making a chart about which animal belongs to who.

Tosh - cat

Bianca - frog

Jaela - parrot

Jun - snake

Suzan - turtle

You can get this list easily by reading the question and eliminating all the choices of animals but the turtle, which must belong to Suzan. Now you have to figure out the names of the pets which will help you figure out who Bianca belongs to and what kind of animal she is.

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named ?

Jun - snake - named?

Suzan - turtle - named ?

The name by which they call the turtle is the same as the name of the woman whose pet is Tosh. Suzan's pet is a turtle who can't be named Bianca, Suzan, Jun or Tosh. Jaela is the only name left, so the turtle is named Jaela. Tosh's owner = name of turtle. That must mean that Jaela's pet parrot is named Tosh. So we have

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named Tosh

Jun - snake - named ?

Suzan - turtle - named Jalea

The only name missing is Bianca, Suzan's mother's pet. So Suzan's mother must be Jun who owns a pet snake named Bianca.

== Problem 2 ==

Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

--> 3 people are right handed and 2 are left, it goes to say Bahao and Dylan are right handed (if Tim and Chan use different hands one of them must be right handed); this also leaves Stewart to be left handed (only 2 people are left handed and if one of them is Tim or Chan the other must be Stewart). With 3 people being under 2m tall, Stewart and Chan being the same height must be under 2m (if Dylan and Tim are different height, one must be under 2); leaving Bahao to be over 2m (if only 2 are over and Dylan and Tim are different only one of them can be over 2m leaving Bahao). You know the centre has to be left handed and over 2m. The only person left on the chart is Tim, who has nothing to his name as of yet. Only 2 people can be over 2m and if the centre is left handed it cannot be Bahao. By elimination Dylan is excluded because he is right handed, Chan and Stewart are under 2m. Tim is the only person left you can fit the qualifications. Tim must be Left handed and over 2m.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand -
* Tim -
* Chan - - Under 2m
* Stewart - Left Hand - Under 2m

Since you know the center, who is left handed and over 2m, is Tim, you can fill out the rest of the chart.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand - Under 2m
* Tim - [[ Left Hand - Over 2m - Centre]]
* Chan - Right Hand - Under 2m
* Stewart - Left Hand - Under 2m

== Problem 3 ==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

This question is best answered by using a graph I believe, First I started by putting the players names on the top of a chart and the positions on the side and going through the list and crossing off any of the players that don't fit the qualifications.

Go through the list and cancel qualifications for example
Adam does not like the catcher---he's not the catcher
Ed's sister is engaged to the second baseman---- Ed is not the Second baseman and the second baseman is not a batchelor
going on Pascal and Charles cannot be the pitcher
Ed cannot be the outfielder
Charles Hassan and Adam are shorter than sung
Pascal and Adam are not the short stop
Ed, Pascal Jason the right fielder and the center fielder means they are batchelors making the others married I used M to indicate married and B for Batchelor in my graph
Using Height Marriage and qualifications I was able to deduct and finish this graph

http://co102w.col102.mail.live.com/att/GetAttachment.aspx?tnail=0&messageId=96be92f2-dc13-11df-8bdc-00237de49116&Aux=4|0|8CD3E377DC9AB80||0|0|0|0||&maxwidth=220&maxheight=160&size=Att[[File:IMG0022-20101019-2329.jpg]]

so the graph came out really small so it will be submitted as written work on wednesday

== Problem 4 ==

Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?

== Problem 5 ==

'''Question:
Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.

On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.

On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.

On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.

In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.

The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.

No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?'''

''Answer:''

[[Step 1]]: First make a list of every day Homer is on vacation.

Saturday:

Sunday:

Monday:

Tuesday:

Wednesday:

Thursday:

Friday:

Saturday (2):

Sunday (2):

[[Step 2:]] Fill in all the information given.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday:

Friday:

Saturday (2): Construction

Sunday (2): Dog

[[Step 3:]] Once the information given is filled in one can see that there are only three possible days that Homer could have slept in during his vacation. We are told that the none of the noise makers stayed quiet for three days straight. Thus based on the salesman noise on wednesday they would have to make noise friday or saturday, because we are also given the information that no noisemaker pairs made noise more then once. If the salesman made noise on the second saturday he would be paired with the construction workers for the second time. From this we can determine the salesman woke Homer up on Friday. Similarly the construction worker woke Homer up on monday which means he woke him up again on either Tuesday or Thursday (sticking with the information no noisemaker didn't make noise for three days straight). Based on this information the construction worker would then have to wake him up on Thursday, if he woke him up on Tuesday there would be a three day discrepancy.

[[Step 4:]] Fill in the remaining information found through your thought process above. When done it is easy to see the only day Homer can sleep in is tuesday.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday: Construction

Friday: Salesman

Saturday (2): Construction

Sunday (2): Dog

[[Step 5:]] Homer will be able to actually sleep in on the tuesday of his vacation.

Course:MATH110/Archive/2010-2011/003/Groups/Group 06/Homework 4

2010-10-20T06:39:09Z

MatthewRobinson: /* Problem 3 */

== Problem 1 ==

Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?

Tosh owns a cat, Bianca owns a frog that she loves, Jaela owns a parrot which keeps calling her "darling, darling", Jun owns a snake, don't mess with him, Suzan is the name of the frog, The cat is named Jun, The name by which they call the turtle is the name of the woman whose pet is Tosh, Finally, Suzan's mother's pet is Bianca.

At first this might seem puzzling because it looks as though there are six people because Suzan's mother might be another person. How they've worded the question seems to hint that one of the 5 people who isn't Suzan is her mother.

The second way you could approach the problem would be to eliminate all of the choices with logic and narrow down the corresponding names to what type of pet Suzan's mother owns. Susan's mother could be any of these people because you don't want to assume Tosh or Jun are men.

So you could start by making a chart about which animal belongs to who.

Tosh - cat

Bianca - frog

Jaela - parrot

Jun - snake

Suzan - turtle

You can get this list easily by reading the question and eliminating all the choices of animals but the turtle, which must belong to Suzan. Now you have to figure out the names of the pets which will help you figure out who Bianca belongs to and what kind of animal she is.

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named ?

Jun - snake - named?

Suzan - turtle - named ?

The name by which they call the turtle is the same as the name of the woman whose pet is Tosh. Suzan's pet is a turtle who can't be named Bianca, Suzan, Jun or Tosh. Jaela is the only name left, so the turtle is named Jaela. Tosh's owner = name of turtle. That must mean that Jaela's pet parrot is named Tosh. So we have

Tosh - cat - named Jun

Bianca - frog - named Suzan

Jaela - parrot named Tosh

Jun - snake - named ?

Suzan - turtle - named Jalea

The only name missing is Bianca, Suzan's mother's pet. So Suzan's mother must be Jun who owns a pet snake named Bianca.

== Problem 2 ==

Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

--> 3 people are right handed and 2 are left, it goes to say Bahao and Dylan are right handed (if Tim and Chan use different hands one of them must be right handed); this also leaves Stewart to be left handed (only 2 people are left handed and if one of them is Tim or Chan the other must be Stewart). With 3 people being under 2m tall, Stewart and Chan being the same height must be under 2m (if Dylan and Tim are different height, one must be under 2); leaving Bahao to be over 2m (if only 2 are over and Dylan and Tim are different only one of them can be over 2m leaving Bahao). You know the centre has to be left handed and over 2m. The only person left on the chart is Tim, who has nothing to his name as of yet. Only 2 people can be over 2m and if the centre is left handed it cannot be Bahao. By elimination Dylan is excluded because he is right handed, Chan and Stewart are under 2m. Tim is the only person left you can fit the qualifications. Tim must be Left handed and over 2m.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand -
* Tim -
* Chan - - Under 2m
* Stewart - Left Hand - Under 2m

Since you know the center, who is left handed and over 2m, is Tim, you can fill out the rest of the chart.

* Bahao - Right Hand - Over 2m
* Dylan - Right Hand - Under 2m
* Tim - [[ Left Hand - Over 2m - Centre]]
* Chan - Right Hand - Under 2m
* Stewart - Left Hand - Under 2m

== Problem 3 ==

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,

Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

This question is best answered by using a graph I believe, First I started by putting the players names on the top of a chart and the positions on the side and going through the list and crossing off any of the players that don't fit the qualifications.

Go through the list and cancel qualifications for example
Adam does not like the catcher---he's not the catcher
Ed's sister is engaged to the second baseman---- Ed is not the Second baseman and the second baseman is not a batchelor
going on Pascal and Charles cannot be the pitcher
Ed cannot be the outfielder
Charles Hassan and Adam are shorter than sung
Pascal and Adam are not the short stop
Ed, Pascal Jason the right fielder and the center fielder means they are batchelors making the others married I used M to indicate married and B for Batchelor in my graph
Using Height Marriage and qualifications I was able to deduct and finish this graph

http://co102w.col102.mail.live.com/att/GetAttachment.aspx?tnail=0&messageId=96be92f2-dc13-11df-8bdc-00237de49116&Aux=4|0|8CD3E377DC9AB80||0|0|0|0||&maxwidth=220&maxheight=160&size=Att[[File:IMG0022-20101019-2329.jpg]]

== Problem 4 ==

Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?

== Problem 5 ==

'''Question:
Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.

On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.

On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.

On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.

In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.

The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.

No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?'''

''Answer:''

[[Step 1]]: First make a list of every day Homer is on vacation.

Saturday:

Sunday:

Monday:

Tuesday:

Wednesday:

Thursday:

Friday:

Saturday (2):

Sunday (2):

[[Step 2:]] Fill in all the information given.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday:

Friday:

Saturday (2): Construction

Sunday (2): Dog

[[Step 3:]] Once the information given is filled in one can see that there are only three possible days that Homer could have slept in during his vacation. We are told that the none of the noise makers stayed quiet for three days straight. Thus based on the salesman noise on wednesday they would have to make noise friday or saturday, because we are also given the information that no noisemaker pairs made noise more then once. If the salesman made noise on the second saturday he would be paired with the construction workers for the second time. From this we can determine the salesman woke Homer up on Friday. Similarly the construction worker woke Homer up on monday which means he woke him up again on either Tuesday or Thursday (sticking with the information no noisemaker didn't make noise for three days straight). Based on this information the construction worker would then have to wake him up on Thursday, if he woke him up on Tuesday there would be a three day discrepancy.

[[Step 4:]] Fill in the remaining information found through your thought process above. When done it is easy to see the only day Homer can sleep in is tuesday.

Saturday: Salesman

Sunday: Dog

Monday: Salesman+Construction

Tuesday:

Wednesday: Salesman+Dog

Thursday: Construction

Friday: Salesman

Saturday (2): Construction

Sunday (2): Dog

[[Step 5:]] Homer will be able to actually sleep in on the tuesday of his vacation.

Course:MATH110/Archive/2010-2011/003/Groups/Group 06

2010-10-18T08:21:43Z

MatthewRobinson:

{{Infobox MATH110 Groups
| group number = 6
| member 1 = Nickolas Coker
| member 2 = Gracie Mann
| member 3 = [[User:DerekMoore|Derek Moore]]
| member 4 = [[User:MatthewRobinson|Matthew Robinson]]
| member 5 = [[User:StephanieUrness|Stephanie Urness]]
| member 6 = [[User:ClaireWilliams|Claire Williams]]
}}

Stephanie Urness! email Surness091@gmail.com and phone # 778-837-2898

My email and cell number:
fiveflip@interchange.ubc.ca
604-762-6133
If anyone would like the glorious task of calling me at 8.00 if I have failed to make it to class...
-Derek

Claire Williams!
ctwilliams91@gmail.com 604 838 2701

hi guys its matt robinson I just talked to david and there was a mix up with the groups but im in this one now sooo.. give me a shout what I should do for the hw assignment on wednesday 778 386 7994 matt_robinson77@hotmail.com

Hey! Lets put our homework under a different page, if you click discussion (near the top of the page, the tab to the right of "course") it'll take you to a different page just to keep things from getting to cluttered...let me know if this works! - Steph

Nickolas here. Just give me work and I'm more then happy to do it :) (778)322-7570, coker92@interchange.ubc.ca

==Homework 4==

Problem 3

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
Adam does not like the catcher,
Ed's sister is engaged to the second baseman,
The centre fielder is taller than the right fielder,
Hassan and the third baseman live in the same building,
Pascal and Charles each won $20 from the pitcher at a poker game,
Ed and the outfielders play cards during their free time,
The pitcher's wife is the third baseman's sister,
All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
Pascal, Adam and the shortstop lost $100 each at the race track,
The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
Sung is in the process of getting a divorce,
The catcher and the third baseman each have two legitimate children,
Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
The shortstop, the third baseman and Bobo all attended the fight,
Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.
Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

==Homework 3==

1) A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain. -->Write down all known data given in the equation and draw a picture if possible.
Trip to terminal via bus
•Velocity = 30miles/hr
* Change to m/s – 30miles/hr x 1hr/3600sec x 1600miles/metre = 13.333m/s
•Time = 1 hr and 20 min.
* Change to seconds - 1 hr = 60 min. 60 min + 20 min = 80 min x 60sec/1min = 4800seconds.
Trip returning from terminal via bus
•Velocity = 30 miles/hr
* Like above change to m/s = 13.3m/s
•Time = 80 min
* Change to seconds – 80min x 60seconds/1min = 4800seconds.
→ Look at your data and ensure all units are similar. If they are not, change to similar units. This ensures your answer in the end will not end up with units you are not familiar with or have to change throughout the equation multiple times. Write down the units each time you use them in a calculation, allowing you to go back and check where and if any mistakes have been made when calculating or cancelling out units. The questions asks why one bus took an hour and 20min, while the other only took 80 min. When you change them to similar units (seconds) you see they are the exact same time with different units. This is an easy way to make mistakes and ending up with the wrong number in the end or making the problem more difficult than need be. You ask yourself what am I looking for? The time of each bus trip. If theory if they are traveling at the same speed along the same route they should have the same time for travel – ignoring outside variances. Change units and this confirms your thought.

2) A lady did not have her liscence when she failed to stop at a stop sign and proceeded 3 blocks down a one way in the wrong direction. A policeman did see her but did not stop her. Why?
Information known: She ran a stop sign and drove down a one way for 3 blocks in the wrong direction. Question – why wouldn’t a policeman stop here.
Look at your assumptions – she was driving, maybe the policeman was lazy and let her off, was she driving recklessly.
Reread your question with those assumptions in mind, are they confirmed anywhere ?
It states she “failed” to stop, not that she ran. She “went” 3 blocks, not drove. Always think of the assumptions your are making and see if they make sense/any data to back them up.
→ The only thing to make sense for the policeman not stopping her would be because she is NOT driving. Walking/running or biking maybe.
Reread the question/statement with the thought of her walking in mind, does it make sense? YES.

3) One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.
Draw a picture of each box and label each of the boxes with oranges, apples and apples and oranges.
You want to know the correct labels and how to find out. Which box should you draw from first? Does it make a difference?
If you draw from the box labeled oranges and apples first and get an apple. It goes to say that this box must be “only apples”, as it is the only label that works other than the one it is already labeled with, but the question/statement clearly says they are incorrectly labeled, so by elimination it goes to say it is “Apples only”.
You have two boxes left. One labeled “oranges” and the other “apples”. You do not even need to continue selecting fruit, you should be able to decipher by elimination now. If this label is incorrect, the only other label it can possibly be is just oranges. You can ask why can’t it be “oranges and apples”? Because if it were than the 3rd box labeled oranges would have to be just that, once again the labels are incorrect, so it cannot. This third box must be “apples and oranges”.
Check → You can draw from that both boxes, from your box originally labeled “apples” you will draw an orange confirming your guess. The box labeled “oranges”, you will select either an apple or an orange, what you select doesn’t tell you much but that makes sense because it could be either.

4) I am the brother of the blind fiddler, but brothers I have none. How can this be?
Questions to ask? Who is the fiddler, male or female? Remember assumptions are not always right and may affect how you interpret the question.
If the fiddler were a male, would this statement make sense?
If the fiddler were a female would this statement make sense?
Reread the statement with each of these thoughts in mind, there is nothing saying the fiddler is a male, and it would only make sense if the blind fiddler were a female.
Draw a picture and describe relationships to each other if need be and you can see how the fiddler being a female works with the statement.

5) Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?
What information is known? What are you trying to find out? You can see you are dealing with two circular objects of the same size, one lying flat and the other being rolled around the edge of the one lying flat.
The “same size” clue gives you all the information needed. Diameter of circular objects = the same, therefore the circumferences = same.
If you are rolling the object on its edge around the edges of the other “same sized” object while its lying flat on the counter, you can only assume the times it will revolve is one. Since they are the same size it will not take any longer or any shorter of a distance to go around something of the same distance as its circumference.
Check = grab two quarters, try it out.

6) Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?
You have a box full of 3 different types of apples, you want to know how many times must you draw in order to draw two of the same kind. Does it matter how many apples there are in total?
How many times can you pick apples from the box without picking the same one twice? Because there are 3 different kinds of apples, you can draw 3 times with a chance of coming up with a different apple each time. Now you have exhausted that option, the next apple you draw will have no choice but to be the same kind as one of the previous ones.
Therefore, you see drawing 3 apples will give not be enough to ensure you draw one kind twice but drawing 4 apples will guarantee you draw one type of apple twice.

7) Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same color, and (ii) a pair with different colors?
i) If you draw 3 sox from the drawer two of them will be the same color. ii)You have to draw 40 sox from the drawer because even though it is extremely unlikely you could draw 40 of the same color sox in the drawer.

8)Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible. Reubens birthday is on Dec. 31st. On Dec. 30th 2010 Reuben is 20 years old. On the 31st he turns 21. On January 1st he say "two days ago i was 20 years old next year I am 23." Next December 31st 2011 he turns 22 and LATER in 2012 he turns 23

9) A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises 5 feet, how many rungs will be showing? Understand: Draw a picture of a boat that is able to be affected by the tides (must be floating on the ocean). Ten rungs of the ladder are showing. Variable: The tide rises 5 feet. Solution: the boat is still floating because no variable introduced suggests that the boat has sunk. Therefore - 10 rungs are still showing.

10) Suppose 1/2 of all people are chocolate eaters and 1/2 of all people are women. (1) Does it follow that one fourth of all women are chocolate eaters? (2) Does it follow that one half of all men are chocolate eaters? Explain. Understand: All people suggest a population of people. This can be interpreted as any group. Suddenly, half of all people are women. This forces the population to be half women and half ~women (not women). Half of all people are chocolate eaters. Half of the population (composed of half women, half ~women) are chocolate eaters. I picture this by imagining two different coloured circles (red and blue), one superimposed over the other. Each circle is bisected into 2 equal parts. The red circle represents women (shaded) and ~women (not shaded). The blue circle represents chocolate eaters (shaded) and ~chocolate eaters (not shaded). Notice that the circles, when one is rotated, the colour mix moves with it - the circles are not locked together; they do not necessarily spin together. 1. Does it follow that 1/4 of all women are chocolate eaters? No. It doesn't. This problem suggests no linkage between (chocolate eaters, ~chocolate eaters) and (women, ~women). 2. Does it follow that 1/2 of all men are chocolate eaters? No. Same as above.

11) A woman, her older brother, her son, and her daughter, are chess players. The worst player's twin, who is one of the four players, is the best player of the opposite sex. The worst player and the best player have the same age, who is the worst player? Understand: Draw the family. Assign them ages by changing their heights tallest(oldest). Assume that there is a twin. Logically infer: what is a twin, who in this group is capable of being a twin? Twins are born at the same time. The mother has an older brother, therefore the mother and the older brother cannot be the twins. The woman's children must be the twins. At this point, we know everyone's sex and everyone's age relative to the other members of the group. The characteristics defining who the best and worst players are are these: [the worst player has a twin] [the worst and best players have the same age]. From these, we can infer that the worst and best players are the children (because only they can have the same ages in the group). Unfortunately, that is as far as we can go in determining who are the best and worst players because the determining characteristics to not suggest which sex either explicitly is. This exhausts the two things we know of each member of the group (relative age and sex).

12) A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation. The manhattan fellow is taking trains that are arriving, not departing. The question says nothing of the other girlfriend, who is probably equally as annoyed with the manhattan fellow because she never sees him either. The premises of the problem, specifically [(A manhattan fellow) decided which girlfriend to visit by arriving randomly at the train station and taking the first of the bronx or brooklyn trains that arrived] do not explicitly state that the trains that arrive at the station then proceed to depart the station. The logical explanation is that the premises of the problem do not suggest either girlfriend being satisfied.

13) If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)? The problem does not suggest exactly what the time delay between the 10:00-strike chimes is as the 5:00-strike chimes is stated (at 5 sec/5 chimes = 1 sec/chime). The chime at 10:00 could be a faster set of chimes, perhaps 10 chimes over 3 seconds?

14) One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly? Identify the babies (w,x,y,z). Identify the names (w,x,y,z). (Baby,Name). Only one of each baby and one of each name tag exists. When correctly tagged, (w,w), (x,x), (y,y), (z,z). i. two babies tagged correct, two incorrect. if (w,w) and (x,x), then (y,z) and (z,y). Cases: 6 unique cases because w|x,y,z x|y,z y|z z|(none) 2. If three of the babies are correctly tagged then the last baby cannot be uncorrectly tagged (can only be correctly tagged), because each the babies and the name tags are mutually exclusive when paired (babies cannot share name tags, only one of each baby and name tag exist). Three correctly tagged babies would result in one tag left for one baby. As 3/4 tags were correct, it follows that the 1/4 tag remaining must be correct. Case: (x,x) correct! (w,w) correct! (y,y) correct! z is tagged with what? (z,z) because z is the only baby remaining. (z,z) is correct!

15) Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?
Tell Alex to get a job because you should not take this bet. There are 52 cards in a deck and if you split the deck in 2 there are 26 cards. If you have 12 black cards and 14 red cards in the first half you will automatically have 14 black cards and 12 red cards. This happens because there are 26 black and red cards and that is the whole deck. And if you split the deck in half and count 12 black cards you know in the other half there will be 14 black cards and that works for red cards aswell.
16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?
Well this is quite a large family. There are 4 daughters and 3 brothers. Look at the specifications in the question and they fit.

17. The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.
The only conclusion I can see is that even if the scale was set too low or too high, the combined weights (which may be false) should still add up if the scale is still set to its wrong setting.

18)Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?
If you have x pennies, you remove a third of the x, then you're left with y pennies. You subtract a third of the y pennies, which leaves you with z pennies. subtracting a third of the z pennies will leave you with 40 pennies. You can make an equation, to find x,y,z. You keep plugging in values into each previous equation to find these values. I worked backwards once I got the answers and saw that I ended up with 40. 135 pennies were there at the start.

19)One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?
Since the number of people that drink coffee in the morning drink the same amount of liquid, you can make a formula where m is milk in oz,and c is coffee oz and n is the number of people. m divided by four (because angela drinks a quarter of the total milk) plus c divided by six (she drinks a sixth of the total coffee) multiplied by n which equals the total amount of milk plus coffee. the number of people is at least 5. the only way you can have a positive answer is by making equal to five since you cannot have a negative number of people!

20)Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?
When it is midnight, after each hour the fast clock will gain five minutes more than it normally would. 1:05 becomes 2:10, which goes to 3:15, etc. This is the same for the slow clock except it goes backwards. After an hour it should have gone to 1 oclock but it is only at 12:55. At 6:30 for the fast clock it will only be 5:30 on the slow clock.

21)Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?
If Sven is right in the middle, there has to be equal numbers of people before him or after him. If Dan is slower than Sven in 10th place, Sven could be ninth. With equal numbers on both sides that equals seventeen including Lars, who is 16th.

22)During a vacation, it rained on 13 days, but when it rained in the morning, the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?
You can make rainy mornings, rainy afternoons and sunny in both three variables: x,y,z respectively. Using the terms given, you can make a system of equations. This is the only way that seems possible. The wording was confusing and it was not clear whether or not there were entire days that were sunny.

23)Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.
Paula is clearly a nut. 1)We do not know the date she is referring to. 2)Red hair, besides being unattractive, does not tell give us numerical information about their ages.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?
Make both candles = 12 cm to make it easy. And also lets call the 6hr candle A and the 3 hr candle B. Now we must determine the cm per hour so divide 12 by 6 to get 2cm/h and 12 by 3 to get 4cm/h. Now in the first hour candle A becomes 10cm and B becomes 8 cm. In the second hour candle A becomes 8cm and candle B becomes 4cm. So it takes two hours for it to equal half.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Course talk:MATH110/003/Groups/Group 06

2010-10-13T05:53:33Z

MatthewRobinson:

==Remarks==
Hey guys, I suggest to organise your pages in the wiki in a way that makes a bit more sense and keep it tidy. What about you write the solutions of these problems on your page and we keep the discussion page for discussions?<br/>
-- [[User:DavidKohler|DavidKohler]]
----

Hey everyone! Here is a page we can display our solutions on for the homework due on Wednesday, cheers. - Stephanie

1) A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.
-->Write down all known data given in the equation and draw a picture if possible.
Trip to terminal via bus
•Velocity = 30miles/hr
* Change to m/s – 30miles/hr x 1hr/3600sec x 1600miles/metre = 13.333m/s
•Time = 1 hr and 20 min.
* Change to seconds - 1 hr = 60 min. 60 min + 20 min = 80 min x 60sec/1min = 4800seconds.

Trip returning from terminal via bus
•Velocity = 30 miles/hr
* Like above change to m/s = 13.3m/s
•Time = 80 min
* Change to seconds – 80min x 60seconds/1min = 4800seconds.
→ Look at your data and ensure all units are similar. If they are not, change to similar units. This ensures your answer in the end will not end up with units you are not familiar with or have to change throughout the equation multiple times. Write down the units each time you use them in a calculation, allowing you to go back and check where and if any mistakes have been made when calculating or cancelling out units. The questions asks why one bus took an hour and 20min, while the other only took 80 min. When you change them to similar units (seconds) you see they are the exact same time with different units. This is an easy way to make mistakes and ending up with the wrong number in the end or making the problem more difficult than need be. You ask yourself what am I looking for? The time of each bus trip. If theory if they are traveling at the same speed along the same route they should have the same time for travel – ignoring outside variances. Change units and this confirms your thought.

2) A lady did not have her liscence when she failed to stop at a stop sign and proceeded 3 blocks down a one way in the wrong direction. A policeman did see her but did not stop her. Why?
* Information known: She ran a stop sign and drove down a one way for 3 blocks in the wrong direction. Question – why wouldn’t a policeman stop here.
* Look at your assumptions – she was driving, maybe the policeman was lazy and let her off, was she driving recklessly.
* Reread your question with those assumptions in mind, are they confirmed anywhere ?
* It states she “failed” to stop, not that she ran. She “went” 3 blocks, not drove. Always think of the assumptions your are making and see if they make sense/any data to back them up.
→ The only thing to make sense for the policeman not stopping her would be because she is NOT driving. Walking/running or biking maybe.
* Reread the question/statement with the thought of her walking in mind, does it make sense? YES.

3) One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

* Draw a picture of each box and label each of the boxes with oranges, apples and apples and oranges.
* You want to know the correct labels and how to find out. Which box should you draw from first? Does it make a difference?
* If you draw from the box labeled oranges and apples first and get an apple. It goes to say that this box must be “only apples”, as it is the only label that works other than the one it is already labeled with, but the question/statement clearly says they are incorrectly labeled, so by elimination it goes to say it is “Apples only”.
* You have two boxes left. One labeled “oranges” and the other “apples”. You do not even need to continue selecting fruit, you should be able to decipher by elimination now. If this label is incorrect, the only other label it can possibly be is just oranges. You can ask why can’t it be “oranges and apples”? Because if it were than the 3rd box labeled oranges would have to be just that, once again the labels are incorrect, so it cannot. This third box must be “apples and oranges”.
* Check → You can draw from that both boxes, from your box originally labeled “apples” you will draw an orange confirming your guess. The box labeled “oranges”, you will select either an apple or an orange, what you select doesn’t tell you much but that makes sense because it could be either.

4) I am the brother of the blind fiddler, but brothers I have none. How can this be?
* Questions to ask? Who is the fiddler, male or female? Remember assumptions are not always right and may affect how you interpret the question.
* If the fiddler were a male, would this statement make sense?
* If the fiddler were a female would this statement make sense?
* Reread the statement with each of these thoughts in mind, there is nothing saying the fiddler is a male, and it would only make sense if the blind fiddler were a female.
* Draw a picture and describe relationships to each other if need be and you can see how the fiddler being a female works with the statement.

5) Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?
* What information is known? What are you trying to find out? You can see you are dealing with two circular objects of the same size, one lying flat and the other being rolled around the edge of the one lying flat.
* The “same size” clue gives you all the information needed. Diameter of circular objects = the same, therefore the circumferences = same.
* If you are rolling the object on its edge around the edges of the other “same sized” object while its lying flat on the counter, you can only assume the times it will revolve is one. Since they are the same size it will not take any longer or any shorter of a distance to go around something of the same distance as its circumference.
* Check = grab two quarters, try it out.

6) Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?

* You have a box full of 3 different types of apples, you want to know how many times must you draw in order to draw two of the same kind. Does it matter how many apples there are in total?
* How many times can you pick apples from the box without picking the same one twice? Because there are 3 different kinds of apples, you can draw 3 times with a chance of coming up with a different apple each time. Now you have exhausted that option, the next apple you draw will have no choice but to be the same kind as one of the previous ones.
* Therefore, you see drawing 3 apples will give not be enough to ensure you draw one kind twice but drawing 4 apples will guarantee you draw one type of apple twice.

7) Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same color, and (ii) a pair with different colors?

i) If you draw 3 sox from the drawer two of them will be the same color.
ii)You have to draw 40 sox from the drawer because even though it is extremely unlikely you could draw 40 of the same color sox in the drawer.

8)Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.
Reubens birthday is on Dec. 31st. On Dec. 30th 2010 Reuben is 20 years old. On the 31st he turns 21. On January 1st he say "two days ago i was 20 years old next year I am 23." Next December 31st 2011 he turns 22 and LATER in 2012 he turns 23

15) Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

*Tell Alex to get a job because you should not take this bet. There are 52 cards in a deck and if you split the deck in 2 there are 26 cards. If you have 12 black cards and 14 red cards in the first half you will automatically have 14 black cards and 12 red cards. This happens because there are 26 black and red cards and that is the whole deck. And if you split the deck in half and count 12 black cards you know in the other half there will be 14 black cards and that works for red cards aswell.

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

*Well this is quite a large family. There are 4 daughters and 3 brothers. Look at the specifications in the question and they fit.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?
* Make both candles = 12 cm too make it easy. And also lets call the 6hr candle A and the 3 hr candle B. Now we must determine the cm per hour so divide 12 by 6 to get 2cm/h and 12 by 3 to get 4cm/h. Now in the first hour candle A becomes 10cm and B becomes 8 cm. In the second hour candle A becomes 8cm and candle B becomes 4cm. So it takes two hours for it to equal half.

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Course talk:MATH110/003/Groups/Group 06

2010-10-13T04:53:15Z

MatthewRobinson:

Hey everyone! Here is a page we can display our solutions on for the homework due on Wednesday, cheers. - Stephanie

1) A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.
-->Write down all known data given in the equation and draw a picture if possible.
Trip to terminal via bus
•Velocity = 30miles/hr
* Change to m/s – 30miles/hr x 1hr/3600sec x 1600miles/metre = 13.333m/s
•Time = 1 hr and 20 min.
* Change to seconds - 1 hr = 60 min. 60 min + 20 min = 80 min x 60sec/1min = 4800seconds.

Trip returning from terminal via bus
•Velocity = 30 miles/hr
* Like above change to m/s = 13.3m/s
•Time = 80 min
* Change to seconds – 80min x 60seconds/1min = 4800seconds.
→ Look at your data and ensure all units are similar. If they are not, change to similar units. This ensures your answer in the end will not end up with units you are not familiar with or have to change throughout the equation multiple times. Write down the units each time you use them in a calculation, allowing you to go back and check where and if any mistakes have been made when calculating or cancelling out units. The questions asks why one bus took an hour and 20min, while the other only took 80 min. When you change them to similar units (seconds) you see they are the exact same time with different units. This is an easy way to make mistakes and ending up with the wrong number in the end or making the problem more difficult than need be. You ask yourself what am I looking for? The time of each bus trip. If theory if they are traveling at the same speed along the same route they should have the same time for travel – ignoring outside variances. Change units and this confirms your thought.

2) A lady did not have her liscence when she failed to stop at a stop sign and proceeded 3 blocks down a one way in the wrong direction. A policeman did see her but did not stop her. Why?
* Information known: She ran a stop sign and drove down a one way for 3 blocks in the wrong direction. Question – why wouldn’t a policeman stop here.
* Look at your assumptions – she was driving, maybe the policeman was lazy and let her off, was she driving recklessly.
* Reread your question with those assumptions in mind, are they confirmed anywhere ?
* It states she “failed” to stop, not that she ran. She “went” 3 blocks, not drove. Always think of the assumptions your are making and see if they make sense/any data to back them up.
→ The only thing to make sense for the policeman not stopping her would be because she is NOT driving. Walking/running or biking maybe.
* Reread the question/statement with the thought of her walking in mind, does it make sense? YES.

3) One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

* Draw a picture of each box and label each of the boxes with oranges, apples and apples and oranges.
* You want to know the correct labels and how to find out. Which box should you draw from first? Does it make a difference?
* If you draw from the box labeled oranges and apples first and get an apple. It goes to say that this box must be “only apples”, as it is the only label that works other than the one it is already labeled with, but the question/statement clearly says they are incorrectly labeled, so by elimination it goes to say it is “Apples only”.
* You have two boxes left. One labeled “oranges” and the other “apples”. You do not even need to continue selecting fruit, you should be able to decipher by elimination now. If this label is incorrect, the only other label it can possibly be is just oranges. You can ask why can’t it be “oranges and apples”? Because if it were than the 3rd box labeled oranges would have to be just that, once again the labels are incorrect, so it cannot. This third box must be “apples and oranges”.
* Check → You can draw from that both boxes, from your box originally labeled “apples” you will draw an orange confirming your guess. The box labeled “oranges”, you will select either an apple or an orange, what you select doesn’t tell you much but that makes sense because it could be either.

4) I am the brother of the blind fiddler, but brothers I have none. How can this be?
* Questions to ask? Who is the fiddler, male or female? Remember assumptions are not always right and may affect how you interpret the question.
* If the fiddler were a male, would this statement make sense?
* If the fiddler were a female would this statement make sense?
* Reread the statement with each of these thoughts in mind, there is nothing saying the fiddler is a male, and it would only make sense if the blind fiddler were a female.
* Draw a picture and describe relationships to each other if need be and you can see how the fiddler being a female works with the statement.

5) Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?
* What information is known? What are you trying to find out? You can see you are dealing with two circular objects of the same size, one lying flat and the other being rolled around the edge of the one lying flat.
* The “same size” clue gives you all the information needed. Diameter of circular objects = the same, therefore the circumferences = same.
* If you are rolling the object on its edge around the edges of the other “same sized” object while its lying flat on the counter, you can only assume the times it will revolve is one. Since they are the same size it will not take any longer or any shorter of a distance to go around something of the same distance as its circumference.
* Check = grab two quarters, try it out.

6) Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?

* You have a box full of 3 different types of apples, you want to know how many times must you draw in order to draw two of the same kind. Does it matter how many apples there are in total?
* How many times can you pick apples from the box without picking the same one twice? Because there are 3 different kinds of apples, you can draw 3 times with a chance of coming up with a different apple each time. Now you have exhausted that option, the next apple you draw will have no choice but to be the same kind as one of the previous ones.
* Therefore, you see drawing 3 apples will give not be enough to ensure you draw one kind twice but drawing 4 apples will guarantee you draw one type of apple twice.

7) Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting (i) a pair of the same color, and (ii) a pair with different colors?

i) If you draw 3 sox from the drawer two of them will be the same color.
ii)You have to draw 40 sox from the drawer because even though it is extremely unlikely you could draw 40 of the same color sox in the drawer.

8)Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.
Reubens birthday is on Dec. 31st. On Dec. 30th 2010 Reuben is 20 years old. On the 31st he turns 21. On January 1st he say "two days ago i was 20 years old next year I am 23." Next December 31st 2011 he turns 22 and LATER in 2012 he turns 23

15) Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?

*Tell Alex to get a job because you should not take this bet. There are 52 cards in a deck and if you split the deck in 2 there are 26 cards. If you have 12 black cards and 14 red cards in the first half you will automatically have 14 black cards and 12 red cards. This happens because there are 26 black and red cards and that is the whole deck. And if you split the deck in half and count 12 black cards you know in the other half there will be 14 black cards and that works for red cards aswell.

16. Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

*Well this is quite a large family. There are 4 daughters and 3 brothers. Look at the specifications in the question and they fit.

24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

25. Two candles of length L and L + 1 were lit at 6:00 and 4:30, respectively. At 8:30 they had the same length. The longer candle died at 10:30 and the shorter candle died at 10:00. Find L.

Course talk:MATH110/003/Groups/Group 06

2010-10-13T04:34:57Z

MatthewRobinson:

Course talk:MATH110/003/Groups/Group 06

2010-10-13T04:22:03Z

MatthewRobinson:

Course:MATH110/Archive/2010-2011/003/Groups/Group 06

2010-10-10T23:46:26Z

MatthewRobinson:

Group members:
* Nickolas Coker
* Gracie Mann
* Derek Moore
* Stephanie Urness
* Claire Williams

Stephanie Urness! email Surness091@gmail.com and phone # 778-837-2898

My email and cell number:
fiveflip@interchange.ubc.ca
604-762-6133
If anyone would like the glorious task of calling me at 8.00 if I have failed to make it to class...
-Derek

Claire Williams!
ctwilliams91@gmail.com

hi guys its matt robinson I just talked to david and there was a mix up with the groups but im in this one now sooo.. give me a shout what I should do for the hw assignment on wednesday 778 386 7994 matt_robinson77@hotmail.com

User:MatthewRobinson

2010-10-02T19:39:07Z

MatthewRobinson:

User:MatthewRobinson

2010-09-19T21:57:13Z

MatthewRobinson:

I'm Matt Robinson and I hope to either major in economics or political science.

Renes Descartes was born on March 31st 1956 in La Haye en Touraine a city in France, which would later be named Descartes in honor of “The Father of Modern Philosophy.” Descartes had a huge influence on Western Philosophy and Mathematics and was also a physicist, and writer. He is well known for his famous line in his book Discourse on the Method (1637), “I think therefore I am.” He also influenced mathematics through analytical geometry. Analytical geometry or Cartesian geometry is the study of geometry using a coordinate system and the principals of algebra. Analytical geometry is used to define geometrical shapes in a numerical way and getting numerical information from that representation. Descartes lived most of his life in the Dutch Republic and died at the age of 53 he is still a historical figure for his life work especially in mathematics and philosophy.

User:MatthewRobinson

2010-09-18T18:30:19Z

MatthewRobinson: Created page with 'I'm Matt Robinson and I hope to either major in economics or political science.'

I'm Matt Robinson and I hope to either major in economics or political science.