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Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T07:36:43Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''

Example 1:

3/4x +5/6 = 5x - 125/3

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12(3/4x +5/6) = 12(5x -125/3)

Simplify:

12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = 510/51 = 10

'''Example of Solving Quadratic Equation'''

Example 1:

Solve 6x^2 + 11x – 35 = 0.

This may factor, but it looks like it would be a fair amount of work, and I'm feeling a bit mindless and lazy at the moment, so I'll use the Quadratic Formula instead:

-b + or - sqrt(b^2 - 4ac)/2a

x = -(11) + or - sqrt(11)^2 - (4)(6)(-35)/(2)(6)

x = -11 + or - sqrt(121 + 840)/12

x = -11 + or - sqrt961/12

x = -11 + or - 31/12

x = -11 - 31 / 12, -11 + -31/12

x = -42/12, 20/12

x = -7/2, 5/3

The solution is x = –7/2, 5/3

'''Example of Solving Linear Inequalities'''

Example 1:

Solve (2x – 3)/4 < 2.

First, I'll multiply through by 4. Since the "4" is positive, I don't have to flip the inequality sign:

(2x – 3)/4 < 2

(4) × (2x – 3)/4 < (4)(2)

2x – 3 < 8

2x < 11

x < 11/2 = 5.5

'''Example of Solving Quadratic Inequalities'''

Example 1:

Solve x^2 + 2x – 8 < 0.
First, find the zeroes:

x^2 + 2x – 8 = 0

(x + 4)(x – 2) = 0

x = –4 or x = 2

These x-intercepts split the number line into three intervals: x < –4, –4 < x < 2, and x > 2. Since this is a "less than" inequality, I need the intervals where the parabola is below the x-axis. Since the graph of y = x2 + 2x – 8 is a right-side-up parabola, it is below the axis in the middle (between the two intercepts). Since this is an "or equal to" inequality, the boundary points of the intervals (the intercepts themselves) are included in the solution.

Then the solution is: –4 < x < 2

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T07:01:59Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''

Example 1:

3/4x +5/6 = 5x - 125/3

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12(3/4x +5/6) = 12(5x -125/3)

Simplify:

12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = 510/51 = 10

'''Example of Solving Quadratic Equation'''

Example 1:

Solve 6x^2 + 11x – 35 = 0.

This may factor, but it looks like it would be a fair amount of work, and I'm feeling a bit mindless and lazy at the moment, so I'll use the Quadratic Formula instead:

-b + or - sqrt(b^2 - 4ac)/2a

x = -(11) + or - sqrt(11)^2 - (4)(6)(-35)/(2)(6)

x = -11 + or - sqrt(121 + 840)/12

x = -11 + or - sqrt961/12

x = -11 + or - 31/12

x = -11 - 31 / 12, -11 + -31/12

x = -42/12, 20/12

x = -7/2, 5/3

The solution is x = –7/2, 5/3

'''Example of Solving Linear Inequalities'''

Example 1:

Solve (2x – 3)/4 < 2.

First, I'll multiply through by 4. Since the "4" is positive, I don't have to flip the inequality sign:

(2x – 3)/4 < 2
(4) × (2x – 3)/4 < (4)(2)
2x – 3 < 8
2x < 11
x < 11/2 = 5.5

'''Example of Solving Quadratic Inequalities'''

Example 1:

Solve x^2 + 2x – 8 < 0.
First, find the zeroes:

x^2 + 2x – 8 = 0
(x + 4)(x – 2) = 0
x = –4 or x = 2

These x-intercepts split the number line into three intervals: x < –4, –4 < x < 2, and x > 2. Since this is a "less than" inequality, I need the intervals where the parabola is below the x-axis. Since the graph of y = x2 + 2x – 8 is a right-side-up parabola, it is below the axis in the middle (between the two intercepts). Since this is an "or equal to" inequality, the boundary points of the intervals (the intercepts themselves) are included in the solution.

Then the solution is: –4 < x < 2

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T07:01:15Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''

Example 1:

3/4x +5/6 = 5x - 125/3

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12(3/4x +5/6) = 12(5x -125/3)

Simplify:

12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = 510/51 = 10

'''Example of Solving Quadratic Equation'''

Example 1:

Solve 6x^2 + 11x – 35 = 0.

This may factor, but it looks like it would be a fair amount of work, and I'm feeling a bit mindless and lazy at the moment, so I'll use the Quadratic Formula instead:

-b + or - sqrt(b^2 - 4ac)/2a

x = -(11) + or - sqrt(11)^2 - (4)(6)(-35)/(2)(6)

x = -11 + or - sqrt(121 + 840)/12

x = -11 + or - sqrt961/12

x = -11 + or - 31/12

x = -11 - 31 / 12, -11 + -31/12

x = -42/12, 20/12

x = -7/2, 5/3

The solution is x = –7/2, 5/3

'''Example of Solving Linear Inequalities'''

Example 1:

Solve (2x – 3)/4 < 2.

First, I'll multiply through by 4. Since the "4" is positive, I don't have to flip the inequality sign:

(2x – 3)/4 < 2
(4) × (2x – 3)/4 < (4)(2)
2x – 3 < 8
2x < 11
x < 11/2 = 5.5

'''Example of Solving Quadratic Inequalities'''

Example 1:

Solve x2 + 2x – 8 < 0.
First, find the zeroes:

x2 + 2x – 8 = 0
(x + 4)(x – 2) = 0
x = –4 or x = 2

These x-intercepts split the number line into three intervals: x < –4, –4 < x < 2, and x > 2. Since this is a "less than" inequality, I need the intervals where the parabola is below the x-axis. Since the graph of y = x2 + 2x – 8 is a right-side-up parabola, it is below the axis in the middle (between the two intercepts). Since this is an "or equal to" inequality, the boundary points of the intervals (the intercepts themselves) are included in the solution.

Then the solution is: –4 < x < 2

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T06:44:50Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T06:43:14Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''

Example 1:

3/4x +5/6 = 5x - 125/3

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12(3/4x +5/6) = 12(5x -125/3)

Simplify:

12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = 510/51 = 10

'''Example of Solving Quadratic Equation'''

Example 1:

Solve 6x^2 + 11x – 35 = 0.

This may factor, but it looks like it would be a fair amount of work, and I'm feeling a bit mindless and lazy at the moment, so I'll use the Quadratic Formula instead:

x = -(11) + or - sqrt(11)^2 - (4)(6)(-35)/(2)(6)

x = -11 + or - sqrt121 + 840/12

x = -11 + or - sqrt961/12

x = -11 + or - 31/12

x = -11 - 31 / 12, -11 + -31/12

x = -42/12, 20/12

x = -7/2, 5/3

The solution is x = –7/2, 5/3

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T06:28:49Z

ByronPinzon: /* Learning Outcomes With Regards To Equations */

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''
Example 1:

3/4x +5/6 = 5x - 125/3

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12(3/4x +5/6) = 12(5x -125/3)

Simplify:

12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = 510/51 = 10

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-11-12T06:27:53Z

ByronPinzon:

{{Infobox MATH110 Groups
| group number = 7
| member 1 = Byron Godoy Pinzon
| member 2 = Saloumeh Hassanzadeh
| member 3 = Michelle Little
| member 4 = Emily Oates
| member 5 = [[User:JoseTorresTorija|Jose Torres-Torija Cubillas]]
| member 6 =
}}

=Homework 4=

==Question #1==
Ok, so first we assigned the cat to Tosh, the frog to Bianca, the parrot to Jaela, and the snake to Jun. Then, we knew that the cat was named Jun and the frog was named Suzan. The owner of the turtle was the name of the owner of Tosh. So, we discarded Jun (because she was already named after the cat) and Suzan (because she was the name of the frog). That left us with Jaela. So, that means that Tosh is the parrot (because Jaela owns the parrot) and the turtle's name is Jaela. So that left us with Jun naming the snake after Bianca. And we know that Suzan's mother's name is Jun because the question states that her mother's pet's name is Bianca.

In conclusion:
Tosh owns a cat (named Jun)
Bianca owns a frog (named Suzan)
Jaela owns a parrot (named Tosh)
Suzan owns a turtle (named Jaela)
Jun owns a snake (named Bianca)

==Question #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?

Tim

So, this problem is solved by writing out the information:
2 people are left handed, 3 are right handed, 2 are over 2m and 3 are under 2m; Bohao and Dylan = same hand, Tim =/= Chan in hand; Stewart and Chan = same height, Dylan =/= Tim (height)
since Bohao and Dylan have the same hand and Tim and Chan don't, that means that Bohao and Dylan and ONE OF Tim or Chan are right handed.
since Stewart and Chan have the same height and Dylan and Tim don't, that means that Stewart and Chan and ONE OF Tim and Dylan are under 2m tall.

so when correlating this information with each player, you get:

Bahao: right handed, over 2 m tall
Stewart: left handed, under 2m tall
Dylan: right handed, either over / under 2m tall
Tim: either right / left handed, either over / under 2m tall
Chan: either right / left handed, under 2m tall

If the one playing centre is OVER 2m tall and is LEFT handed that takes out Bahao, Stewart, Dylan and Chan by eliminating the factors, so the centre must be Tim.

==Question #3==
Determine the positions of each player on the baseball team.
Outfielders:
center fielder -- Sung
left fielder -- Ed
right fielder -- Bobo
Infielders:
1st baseman -- Pascal
2nd baseman -- Charles
3rd baseman -- Adam
Shortstop -- Jason
Battery:
Pitcher -- Hassan
Catcher -- Mathieu

We determined this by process of elimination and by using the clues to determine what position the players for sure were NOT.

-Clue #1: Adam does not like the catcher --> hence, Adam is NOT the catcher

-Clue #2: Ed's sister is engaged to the second baseman --> the 2nd baseman is NOT single

-Clue #3: The centre fielder is taller than the right fielder --> upon figuring out with later clues that Bobo was the right fielder, it made sense that Sung was center
fielder

-Clue #4: Hassan and the third baseman live in the same building --> Hassan is NOT the third baseman

-Clue #5: Pascal and Charles each won $20 from the pitcher at a poker game --> Neither Pascal or Charles is the pitcher

-Clue #6: Ed and the outfielders play cards during their free time --> thus, Ed is NOT an outfielder

-Clue #7: The pitcher's wife is the third baseman's sister --> the pitcher is married

-Clue #8: All the battery and infield except Charles, Hassan and Adam are shorter than Sung --> Thus, Charles, Hassan, and Adam cannot be in the outfield

-Clue #9: Pascal, Adam and the shortstop lost $100 each at the race track -->Pascal and Adam cannot be the shortstop

-Clue #10: The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards -->Pascal, Hassan nor Bobo can be the catcher OR the 2nd baseman

-Clue #11: Sung is in the process of getting a divorce --> Thus, Sung is SINGLE

-Clue #12: The catcher and the third baseman each have two legitimate children --> the catcher and the 3rd basemen are married

-Clue #13: Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married --> Ed, Pascal, Jason, the right fielder and the center
fielder must not be married

-Clue #14: The shortstop, the third baseman and Bobo all attended the fight --> Bobo cannot be the shortstop or the 3rd baseman

-Clue #15: Mathieu is the shortest player of the team --> he cannot be outfield

Through the process of elimination, we determined the results shown above.
We concluded the following facts about each player:
Adam: could NOT be the catcher, 2nd baseman, right, left, or center outfielder or the shortstop
Bobo: could NOT be the shortstop, 3rd baseman, the catcher, or 2nd baseman
Charles: could NOT be the pitcher, right, left, or center outfielder.
Ed: could NOT be right fielder, center fielder, catcher, 3rd baseman, pitcher or 2nd baseman
Hassan: could NOT be 2nd baseman, catcher, right, left or center outfielder, or 3rd baseman
Jason: could NOT be right fielder, center fielder, 3red baseman, catcher, or pitcher
Mathieu: could NOT be right, left or center outfielder
Pascal: could NOT be pitcher, 2nd baseman, catcher, right fielder, center fielder, 3rd baseman, or shortstop
Sung: single, and tall

From these conclusions about each person, we put each possible candidate next to each position, and by crossing off each name we had found the position for, we solved the puzzle:

Right fielder: Bobo
Left fielder: Ed, Jason, Pascal, Sung, Bobo
Center fielder: Bobo, Sung
1st baseman: Adam, Bobo, Charles, Hassan, Jason, Mathieu, Pascal, Sung
2nd baseman: Charles, Ed, Jason, Mathieu, Sung
3rd baseman: Adam, Charles, Mathieu, Sung
Shortstop: Charles, Hassan, Jason, Mathieu, Sung
Pitcher: Adam, Bobo, Hassan, Mathieu
Catcher: Charles, Mathieu, Sung

==Question #4==
Since you do not know the actual line up of the tournament you must create scenarios were every competitor must play a game versus each other only once. By doing this we can create random matches with players we know are not the “main” attraction and eventually find out who Fernanda will play on the fifth day.

-On the first day, we know that Carla played Petra then that means Fernanda could have played against Sandra, Janet, or Li. So we can set up matches as is Carla vs. Petra, Fernanda vs. Li, Janet vs. Sandra
C.vs.P F.vs.L J.vs.S

-On the second day, we know that Carla played Janet then that means Fernanda could have played Petra, Sandra, or Li. Since on the first day Fernanda and Li already played each other they cannot play each other again so we must put her with Sandra. So the matches are Carla vs. Janet, Fernanda vs. Sandra, and Petra vs. Li
C.vs.J F.vs.S P.vs.L

-On the third day, If Janet played Li then that means Fernanda could have played Petra, Sandra or Carla. Since we know that Fernanda has already played against Sandra we cannot match her up with her so she must play against Petra. So matches are Janet vs. Li, Fernanda vs. Petra, Carla vs. Sandra
J.vs.L F.vs.P C.vs.S

-On the fourth day, If Petra played Sandra then that means Fernanda could have played Carla, Janet or Li. But sense Fernanda already played against Petra and Li she must play Janet because otherwise Carla would play against the same person. Petra vs. Sandra, Fernanda vs. Janet, Carla vs. Li
P.vs.S F.vs.J C.vs.L

-On the firth day since each player only plays each of the others once, the only matches left of are those that involve people not playing each other before hand so the matches are Petra vs. Janet, Li vs. Sandra and Fernanda vs. Carla.
P.vs.J F.vs.C L.vs.S

So on the 5th day Fernanda must play against Sandra

==Question #5==
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?

Salesman = S
Dog = D
Construction Worker = CW
Homer had a vacation from Saturday through to the next Sunday

Saturday -> S

Sunday -> D

Monday -> S+CW

Tuesday ->

Wednesday -> S+D

Thursday -> CW+D

Friday ->

Saturday -> CW+S

Sunday -> D

Homer would get sleep on Tuesday and Friday during his vacation. This will work if every noise maker made noise on the 3rd day of the non-consecutive day period. The Salesmen would have to show up the first Saturday, Monday, Wednesday and then the second Saturday. The dog then makes noise on Sunday, Wednesday, Thursday and Sunday the dog makes noise on 2 consecutive days so that he can pair up with the construction worker. So then the construction worker makes noise on Monday, Thursday and Saturday.

=Homework 5=

==Those That Pose No Problem==
Basic functions,
Basic Properties of Functions,
Equations,
Polynomial Long Division,
Graphs of Functions,
Intersections of Functions,
Reading Graphs of functions,
Distances and Lines,
Operations on Graphs of Functions,
Construction of Graphs,
Trigonometry and the Pythagoras Theorem,
Areas and Volumes,
Mathematical Writing.

==Those That Just Need Practice==
Inequalities and
Composition of Functions

=Basic Skills Learning Guide Project=

==Learning Outcomes With Regards To Equations==
'''Example of Solving Linear Equations'''
Example 1:
3/4x +5/6 = 5x - 125/3
Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.
12(3/4x +5/6) = 12(5x -125/3)
Simplify:
12(3/4x) + 12(5/6) = 12(5x) - 12(125/3)
3(3x) + 2(5) = 60x - 500
9x + 10 = 60x - 500
Subtract 9x from both sides of the equation:
10 = 51x - 500
Add 500 to both sides of the equation:
510 = 51x
Divide both sides by 51:
x = 510/51 = 10

Course:MATH110/Archive/2010-2011/003/Groups/Group 07

2010-10-20T06:41:47Z

ByronPinzon: /* Question #1 */

User:ByronPinzon

2010-09-20T02:35:15Z

ByronPinzon:

I am a second year student currently in the faculty of Human Kinetics. My goal is to become a physiotherapist one day. On my spare time, I like to play all kinds of sports.

Rene Descartes-the father of modern philosophy, as he was called-was born on March 31st 1596. He was a philosopher, mathematician, and a writer. As a result of his work in the field of mathematics, he was called the father of analytical geometry. He not only contributed in just math however, what we call "Western Philosophy" is a direct result of some of his writings, which are still being used as study guides and as resources for reference to this day. His work in the field of analytical geometry though, was where he made his biggest impression. Analytical geometry-also known as cartesian geometry-was the study of geometry by using a coordinate system, algebra, and analysis. This breakthrough by Descartes allowed us to study and quantitatively analyze shapes, line segments, and curved lines. Descartes’s work also led to a breakthrough in calculus: specifically infinitesimal calculus. This branch of mathematics was used to figure out limits and the differentiation and integration of functions.

User:ByronPinzon

2010-09-20T02:08:36Z

ByronPinzon: Created page with 'I am a second year student currently in the faculty of Human Kinetics. My goal is to become a physiotherapist one day. On my spare time, I like to play all kinds of sports.'

I am a second year student currently in the faculty of Human Kinetics. My goal is to become a physiotherapist one day. On my spare time, I like to play all kinds of sports.