UBC Wiki - User contributions [en]

User:MichelleGutmanis

2011-01-28T04:57:09Z

MichelleGutmanis:

My short name is Micha (pronounced me-sha). I am in the Faculty of Forestry and love it, but I am considering switching to Environmental Science next year.

==Parabolae in Our Lives==

Golfball trajectories, water fountains, roller coasters, and swing sets can all be represented by a parabola. Parabolae, a conic section, was first studied by a Greek mathematician named Menaechmus. A conic section is a curve acquired by intersecting a cone with a plane. Menaechmus first came across the parabola by trying to design a way to duplicate the cube, particularly to find the side of a cube that has a volume double that of a given cube. Even though he did not actually name the ‘parabola’, the equation that Menaechmus came up with was: ax² + bx + c, where a, b, and c affect the shape and location and can not be equal to zero. A parabola can be shifted, stretched, compressed, flipped, and translated. Parabolas are one of the most commonly studied subjects in mathematics, and are involved with our everyday lives. When your finished reading my essay and throw your laptop across the room, that can be an example of parabolic motion.

Citations:
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Parabola.html

File:Ticino4.jpg

2011-01-25T23:33:34Z

MichelleGutmanis:

File:Ticino3.jpg

2011-01-25T23:28:49Z

MichelleGutmanis:

File:Ticino2.JPEG

2011-01-25T23:25:22Z

MichelleGutmanis:

File:Ticino2.png

2011-01-25T23:17:36Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T23:09:21Z

MichelleGutmanis:

<math>p(t)=\dfrac{1}{1+e^{-t}}</math>

[[File:Ticino graph 1.png]]

To change the height of the horizontal asymptote to ''k'', we can add ''k'' to the formula as follows:

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-t}}</math>

In order to change the y-intercept of our function, we can add any number, ''q'', where ''q'' is any value between negative infinity and infinity, as shown:

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-t+q}}</math>

BONUS: to change the slope of the function, multiply any number, ''q'', to ''t''

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-8t}}</math>

File:Ticino graph 1.png

2011-01-25T23:06:02Z

MichelleGutmanis:

File:Graph.jpg

2011-01-25T23:05:15Z

MichelleGutmanis: uploaded a new version of "File:Graph.jpg": Reverted to version as of 21:00, 13 October 2010

File:Graph.jpg

2011-01-25T23:04:18Z

MichelleGutmanis: uploaded a new version of "File:Graph.jpg"

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T23:00:23Z

MichelleGutmanis:

<math>p(t)=\dfrac{1}{1+e^{-t}}</math>

To change the height of the horizontal asymptote to ''k'', we can add ''k'' to the formula as follows:

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-t}}</math>

In order to change the y-intercept of our function, we can add any number, ''q'', where ''q'' is any value between negative infinity and infinity, as shown:

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-t+q}}</math>

BONUS: to change the slope of the function, multiply any number, ''q'', to ''t''

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-8t}}</math>

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:59:42Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:42:47Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:28:50Z

MichelleGutmanis:

<math>p(t)=\dfrac{1}{1+e^{-t}}</math>

To change the height of the horizontal asymptote to ''k'', we can add ''k'' to the formula as follows:

<math>p(t)=\dfrac{1}{\tfrac {1}{k}+e^{-t}}</math>

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:26:57Z

MichelleGutmanis:

<math>p(t)=\dfrac{1}{1+e^{-t}}</math>

To change the height of the horizontal asymptote, we can add ''k'' to the formula as follows:

<math>p(t)=\dfrac{\tfrac {1}{k}}{1+e^{-t}}</math>

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:22:01Z

MichelleGutmanis:

<math>p(t)=\dfrac{1}{1+e^{-t}}</math>

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:21:06Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:19:34Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:19:08Z

MichelleGutmanis:

Course:MATH110/Archive/2010-2011/003/Teams/Ticino/Homework 12

2011-01-25T22:18:52Z

MichelleGutmanis:

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

2011-01-25T22:15:50Z

MichelleGutmanis:

{{
Infobox MATH110 Teams
| team name = Ticino
| member 1 = [[User:BenJeffery|BenJeffery]]
| member 2 = [[User:BerndetteHii|BernadetteHii]]
| member 3 = Caitlin Lastiwka-Farquharson
| member 4 = Micha Gutmanis
}}
In workshop M.

===Keywords===

Caitlin - Watermelon

Micha - Music

Bernadette - Purple

Ben - Coffee

===Group Work===

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Ticino/Homework_11 Homework 11]

[http://wiki.ubc.ca/Course:MATH110/003/Teams/Ticino/Homework_12 Homework 12]

Course:MATH110/Archive/2010-2011/003/Math Forum/Webwork Week 11

2011-01-18T22:46:32Z

MichelleGutmanis:

==Question 1==

How do I put 'degrees celsius' into Webwork for the second part of the question? [[User:EllenTsang|EllenTsang]]

Yea Same Question.

I also have the same question!

==Question 2==

Does anyone know how to do problem 11?

==Question 3==

How do you do number 9?

Course:MATH110/Archive/2010-2011/003/Math Forum/Webwork Week 11

2011-01-18T22:26:03Z

MichelleGutmanis: /* Question 1 */

Course:MATH110/Archive/2010-2011/003/Math Forum

2010-12-06T23:48:07Z

MichelleGutmanis:

This space is meant to be organized by the students. The instructor will help organize the wiki, but won't necessarily interfere with the math content.

For example, you could ask more details about the quiz of Lecture 2. Or get some help understanding something from the reading in section 3.1 or 4.2.

==Subpages of the Math Forum==

Once in a while, I'l archive the discussions in subpages, you can find it all on the following pages.

<dpl>
titlematch={{PAGENAME}}/%
namespace={{NAMESPACE}}
shownamespace=false
</dpl>

==Winter Final==

Is there any practice questions or last years winter final that we could use to study?

==Nov.19 Problem 1==

Anybody have any ideas to even start finding the proof? Thanks. 
http://wiki.ubc.ca/images/math/c/6/2/c62af4f5040ad1a27d5f1c9e38731786.png

-adam

==Webwork Week 10==

Does anyone have an helpful tips towards solving for the second derivative below:
Find y" for y= 2(x^2-6)^3

-Ghita Youssefi

:Did you compute <math>y'</math> already?

Try expanding what is in the brackets first, that should make it easier to find the first derivative. Hope this helps.
Steffany

== Rock paper scissors ==
Does anyone have any helpful tips towards solving the question regarding rock-paper-scissors?

== Homework 4: Problem Solving ==
Here's some space to help each other solve these problems. I would appreciate if you kept it at helping each other and not giving away the answer too easily. Struggling and hitting your head against the walls is a healthy way to do mathematics. [[User:DavidKohler|DavidKohler]]

=== Problem 1 ===
=== Problem 2 ===
=== Problem 3 ===
hey guys, ive been giving a shot at question 3 but I have many doubts regarding the wording... in one of the situations, it states that Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married. however, Ed's sister is engaged to the second baseman. does this mean that I can consider the second baseman as married or as a bachelor?

also, consider these two statements:
Pascal and Charles each won $20 from the pitcher at a poker game,
Ed and the outfielders play cards during their free time,
I figured that this would imply that pascal and charles are both outfielders and that Ed is the pitcher. however, this is not the case.
The pitcher can't be Ed since Ed is a bachelor and it states that the pitcher has a wife.

The reason I also brought up Pascal and Charles is because from the previous statement it would seem as if pascal and charles are part of the outfieldiers. We are also told that "All the battery and infield except Charles, Hassan and Adam are shorter than Sung" nulling the fact that charles is an outfielder...

It also states that Sung is in the process of getting divorced. once again can I consider him a bachelor or married? if I still consider him as married. what is the importance of that phrase in the context of the question?
I am extremely confused as to how to take on this question.

If someone could look at it id greatly appreciate it.
Thx

[[User:MarcoGasparian|MarcoGasparian]]

Hey Marco,

I had similar issues with the problem and I still haven't completed but can't contribute a bit here.

Logically, being engaged is not being married. So, I treated the second baseman as a bachelor.

You are right; since Ed is a bachelor, he cannot be the pitcher.

I think this statement might be trying to confuse us a bit. Maybe there are, within the team, different subgroups of card-playing buddies and Ed and the outfielders form one subgroup and Pascal, Charles and the pitcher form the second etc....?

Once again, I treated Sung as a married man because technically he is still married. This information is somewhat relevant in the context of this problem because when you are considering solutions, Sung will be part of the married players. I guess they are just twisting the phrase to confuse us!

Hope this helps at least a little! :D

Arabella.

=== Problem 4===
=== Problem 5===

== A2 Question 10 ==

I gave this question a try but it's not making any more sense:

"The graph of the function f(x)=-4^x can be obtained from the graph of g(x)=4^x by one of the following actions:"

I don't know how the changes are reflected on the graph...I'd say the function has shifted vertically. What would the range for this be? I am lost...a hint please, someone? Thanks kindly.

Arabella.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:45:16Z

MichelleGutmanis: /* Homework Subpages: */

{{Infobox MATH110 Groups
| group number = 10
| member 1 = Anna Koniuhova
| member 2 = [[User:MichelleGutmanis|Michelle Gutmanis]]
| member 3 = Hyun Lee
| member 4 = [[User:AgnesLuong|Agnes Luong]]
| member 5 = [[User:TrevorShumka|Trevor Shumka]]
| member 6 = [[User:RaphaelTan|Raphael Tan]]
}}

=='''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010'''==

'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

'''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?

Considering if there were only 6 apples in the basket with two of each kind, then after six draws one can be sure of getting at least two of one kind.

'''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 the socks were drawn one by one and the pair had to be drawn consecutively, there is a possibility that that may never happen if the socks drawn come out alternatively (considering that once the sock is drawn it is not put back in.

ii) Again, using the same method in part i (drawing the socks one at a time) if all the socks drawn up until the 40th sock were the same color then by the 41st pick you would have drawn a pair of mismatched socks.

'''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.

Reuben was born on January 1st at 12am. Then two days later it would be a new year, he would have turned 21 from 20. Then later in the year he celebrates his birthday again at 12am, turning 22. Then it becomes the next year which means he is 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 five feet, how many rungs will be showing?

If the boat is at least 15 feet tall then all the rungs on the ladder would show, as well if the ladder is hung horizontally then all the rungs would show as well.

'''10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.
Patterns (i) and (ii) will not follow, as we are using the same group of "all people" where one half are all women and one half are all chocolate eaters does not make this exclusive. Meaning that the chocolate eaters can be included in the group of women and vice versa. If the question was phrased as "one half of all people are women while the OTHER half are chocolate eaters" then patterns (i) and (ii) may follow.

''10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.''

(i) It does not follow that ¼ of all of the people are women chocolate eaters because the facts above state that ½ of the total people are women, it does not mean that they all eat chocolate. (ii) Similarly, it does not follow that ½ of men are chocolate eaters. Being a man or woman is independent of preference for chocolate.

''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, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?''

This is not possible because the facts are inconsistent such that the situation doesn’t make sense with the question.

''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.''

If for instance the Bronx train arrives at 10:00, 10:10, 10:20, and the Brooklyn train arrives at 9:59, 10:09, 10:19 then he would take preference over the Brooklyn train and never visit because it arrives earlier.

''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)?''

If you consider the time between chimes then you know it takes 45/4 seconds to strike 10:00.

''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?''

(i) There are six ways that two of the four babies can be correctly tagged. (ii) There are no ways that ¾ of the four babies can be correctly tagged and 1 incorrectly.

''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?''

Alex is correct, you should not accept his bet because naturally the amount of red cards is 50/50 to the amount of black cards in the deck.

'''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?

D = Daughter
S = Son

Daughter has same number of brothers as sisters. Therefore,
D = S + 1

Son has twice as many brothers as sisters. Therefore,
S - 1 = D/2

Combine the equations together to solve for S:

2(S+1 = D/2) = 2S - 2 = D

Since we already know that D = S+1, S + 1 = 2S - 2

To solve for S, isolate S: 2S-S = 1+2
S = 3

We can find D by substituting S into one of the above equations:

Using the equation D = S + 1, D = 3 + 1 D = 4

It can therefore be seen that there are four daughters and three sons.

'''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.

This problem can easily be solved by considering what happens if Dan stands on the scale while sarah is already on it. The scale will read 50 kg with Sarah on the scale and then 110 kg when Dan gets on as well. Since this reading is 5 kg higher than the total reading in the example (105 kg), the scale reads 5kg too high.

'''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?

In this situation, Alice leaves two thirds of a whole, Bret leaves two thirds of two thirds (4/9), and Carla leaves two thirds of four ninths (16/81).

Adding the fractions of the total amount left in the jar, we find that it equals 8/27. Now we need to determine what value of x satisfies the equation that (8/27)x = 40

This can be done by dividing 40 by 8/27. The value for this is 135. Therefore, the jar started with 135 pennies originally.

'''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?

M = Total Milk
C = Total Coffee
A = Angela's Drink
F = Family

A = (1/4)M + (1/6)C
F = (3/4)M + (5/6)C

The least number of people in the family is the number of people required to drink the remaining 5/6 of coffee (5 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?

F = Fast Clock
S = Slow Clock

Both F and S = 5 minutes.

One Hour = 60 Minutes

60 = x (F + S)

aka. the clocks become 10 minutes apart every hour.

60/x = 10

60/10 = x

x = 6

The clocks are therefore an hour apart after six hours.

=='''Homework Subpages:'''==

**not sure if this is how you make the homework page ..

Homework 4:[ http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_10/Homework_4]

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:43:59Z

MichelleGutmanis: /* Homework Subpages: */

{{Infobox MATH110 Groups
| group number = 10
| member 1 = Anna Koniuhova
| member 2 = [[User:MichelleGutmanis|Michelle Gutmanis]]
| member 3 = Hyun Lee
| member 4 = [[User:AgnesLuong|Agnes Luong]]
| member 5 = [[User:TrevorShumka|Trevor Shumka]]
| member 6 = [[User:RaphaelTan|Raphael Tan]]
}}

=='''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010'''==

'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

'''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?

Considering if there were only 6 apples in the basket with two of each kind, then after six draws one can be sure of getting at least two of one kind.

'''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 the socks were drawn one by one and the pair had to be drawn consecutively, there is a possibility that that may never happen if the socks drawn come out alternatively (considering that once the sock is drawn it is not put back in.

ii) Again, using the same method in part i (drawing the socks one at a time) if all the socks drawn up until the 40th sock were the same color then by the 41st pick you would have drawn a pair of mismatched socks.

'''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.

Reuben was born on January 1st at 12am. Then two days later it would be a new year, he would have turned 21 from 20. Then later in the year he celebrates his birthday again at 12am, turning 22. Then it becomes the next year which means he is 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 five feet, how many rungs will be showing?

If the boat is at least 15 feet tall then all the rungs on the ladder would show, as well if the ladder is hung horizontally then all the rungs would show as well.

'''10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.
Patterns (i) and (ii) will not follow, as we are using the same group of "all people" where one half are all women and one half are all chocolate eaters does not make this exclusive. Meaning that the chocolate eaters can be included in the group of women and vice versa. If the question was phrased as "one half of all people are women while the OTHER half are chocolate eaters" then patterns (i) and (ii) may follow.

''10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.''

(i) It does not follow that ¼ of all of the people are women chocolate eaters because the facts above state that ½ of the total people are women, it does not mean that they all eat chocolate. (ii) Similarly, it does not follow that ½ of men are chocolate eaters. Being a man or woman is independent of preference for chocolate.

''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, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?''

This is not possible because the facts are inconsistent such that the situation doesn’t make sense with the question.

''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.''

If for instance the Bronx train arrives at 10:00, 10:10, 10:20, and the Brooklyn train arrives at 9:59, 10:09, 10:19 then he would take preference over the Brooklyn train and never visit because it arrives earlier.

''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)?''

If you consider the time between chimes then you know it takes 45/4 seconds to strike 10:00.

''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?''

(i) There are six ways that two of the four babies can be correctly tagged. (ii) There are no ways that ¾ of the four babies can be correctly tagged and 1 incorrectly.

''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?''

Alex is correct, you should not accept his bet because naturally the amount of red cards is 50/50 to the amount of black cards in the deck.

'''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?

D = Daughter
S = Son

Daughter has same number of brothers as sisters. Therefore,
D = S + 1

Son has twice as many brothers as sisters. Therefore,
S - 1 = D/2

Combine the equations together to solve for S:

2(S+1 = D/2) = 2S - 2 = D

Since we already know that D = S+1, S + 1 = 2S - 2

To solve for S, isolate S: 2S-S = 1+2
S = 3

We can find D by substituting S into one of the above equations:

Using the equation D = S + 1, D = 3 + 1 D = 4

It can therefore be seen that there are four daughters and three sons.

'''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.

This problem can easily be solved by considering what happens if Dan stands on the scale while sarah is already on it. The scale will read 50 kg with Sarah on the scale and then 110 kg when Dan gets on as well. Since this reading is 5 kg higher than the total reading in the example (105 kg), the scale reads 5kg too high.

'''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?

In this situation, Alice leaves two thirds of a whole, Bret leaves two thirds of two thirds (4/9), and Carla leaves two thirds of four ninths (16/81).

Adding the fractions of the total amount left in the jar, we find that it equals 8/27. Now we need to determine what value of x satisfies the equation that (8/27)x = 40

This can be done by dividing 40 by 8/27. The value for this is 135. Therefore, the jar started with 135 pennies originally.

'''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?

M = Total Milk
C = Total Coffee
A = Angela's Drink
F = Family

A = (1/4)M + (1/6)C
F = (3/4)M + (5/6)C

The least number of people in the family is the number of people required to drink the remaining 5/6 of coffee (5 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?

F = Fast Clock
S = Slow Clock

Both F and S = 5 minutes.

One Hour = 60 Minutes

60 = x (F + S)

aka. the clocks become 10 minutes apart every hour.

60/x = 10

60/10 = x

x = 6

The clocks are therefore an hour apart after six hours.

=='''Homework Subpages:'''==

Homework 4:[ http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_10/Homework_4]

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:42:37Z

MichelleGutmanis: /* Homework Subpages: */

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:42:11Z

MichelleGutmanis: /* Homework Subpages: */

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:41:24Z

MichelleGutmanis: /* Homework Subpages: */

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-18T21:40:30Z

MichelleGutmanis: /* Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010 */

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:06:43Z

MichelleGutmanis:

Group members:
* Anna Koniuhova
* Michelle Gutmanis
* Hyun Lee
* Agnes Luong
* Trevor Shumka
* Raphael Tan

=='''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010'''==

'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:05:07Z

MichelleGutmanis:

Group members:
* Anna Koniuhova
* Michelle Gutmanis
* Hyun Lee
* Agnes Luong
* Trevor Shumka
* Raphael Tan

'''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010'''

'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:03:54Z

MichelleGutmanis:

Group members:
* Anna Koniuhova
* Michelle Gutmanis
* Hyun Lee
* Agnes Luong
* Trevor Shumka
* Raphael Tan

'''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010
'''
'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:02:45Z

MichelleGutmanis:

Group members:
* Anna Koniuhova
* Michelle Gutmanis
* Hyun Lee
* Agnes Luong
* Trevor Shumka
* Raphael Tan

'''Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010
'''
'''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.'''

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

'''2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

'''
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.'''

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

'''
4. I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

'''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?'''

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:01:03Z

MichelleGutmanis:

Group members:
* Anna Koniuhova
* Michelle Gutmanis
* Hyun Lee
* Agnes Luong
* Trevor Shumka
* Raphael Tan

Homework 3 - Third Part - Problem Solving Skills - Due date: October 13, 2010

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.

In this problem, two different methods of telling time are used, one is by hours and minutes and the other is just minutes. Since an hour is 60 min, and the problem states that it took an hour and 20 min, this would mean it took 80 min. Therefore, it took 80 min to travel from the terminal to the airport and 80 min to travel from the terminal to the airport each way traveling at a speed of 30mi/hr.

2. A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.

This problem states that a lady did not have her drivers license, failed to stop at a stop sign, and wen three blocks down a one-way street the wrong way without getting stopped - which all are assumed to be things that you should pay attention to while driving. This problem however never mentioned that the woman was driving, so she could have been walking or running. Therefore, the driving rules would not apply to her and she was not breaking the law, so that is why the policeman did not need to stop her.

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.

Since we already know that the labels are incorrect, we could select a fruit the box that says APPLES & ORANGES because that way if an apple is selected, we would know that that box is apples, and the one that says oranges would have to be APPLES & ORANGES because it is labeled incorrectly so it cannot be oranges.

Ex.

Box1 : APPLES & ORANGES
(must be APPLES because it cannot be APPLES & ORANGES, and apples can't go in the ORANGES box)

Box2 : ORANGES
(must be named APPLES & ORANGES because: it cannot be apples since an apple was selected from original APPLES & ORANGES box (box1), and cannot be ORANGES because it is labelled incorrectly)

Box3 : APPLES
(must be ORANGES because: it cannot be APPLES because it is labelled incorrectly, and the original ORANGES box (box2) is now APPLES & ORANGES)

4. I am the brother of the blind fiddler, but brothers I have none. How can this be?

Being a brother could mean that he is the brother of a boy or a girl. Therefore, since he does not have any brothers, the blind fiddler must be his sister.

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?

Since the quarter has to go all the way around the other quarter, if you try it, you will find that it revolves twice. One rotation will get it halfway around the quarter, and the other rotation will bring it to its original position.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10

2010-10-13T04:00:47Z

MichelleGutmanis:

User:MichelleGutmanis

2010-09-20T04:06:22Z

MichelleGutmanis:

My short name is Micha (pronounced me-sha). I am in the Faculty of Forestry and love it, but I am considering switching to Environmental Science next year.

Parabolae in Our Lives

Golfball trajectories, water fountains, roller coasters, and swing sets can all be represented by a parabola. Parabolae, a conic section, was first studied by a Greek mathematician named Menaechmus. A conic section is a curve acquired by intersecting a cone with a plane. Menaechmus first came across the parabola by trying to design a way to duplicate the cube, particularly to find the side of a cube that has a volume double that of a given cube. Even though he did not actually name the ‘parabola’, the equation that Menaechmus came up with was: ax² + bx + c, where a, b, and c affect the shape and location and can not be equal to zero. A parabola can be shifted, stretched, compressed, flipped, and translated. Parabolas are one of the most commonly studied subjects in mathematics, and are involved with our everyday lives. When your finished reading my essay and throw your laptop across the room, that can be an example of parabolic motion.

Citations:
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Parabola.html

User:MichelleGutmanis

2010-09-20T04:03:18Z

MichelleGutmanis: Created page with 'My short name is Micha (pronounced me-sha). I am in the Faculty of Forestry and love it, but I am considering switching to Environmental Science next year. Parabolae in Our Li…'