UBC Wiki - User contributions [en]

User:ShaunaMaty

2011-01-28T05:28:03Z

ShaunaMaty:

''Calculus in Medicine''

In the future, I would like to continue my studies in order to pursue a career in the medical field. Regardless of what component I decide to specialize in, a good basis of calculus will guide me in many facets of this field because of the underlying lessons that come from studying calculus. While calculus is mainly about solving problems, the intrinsic lessons it teaches are a good preparation for the copious amount of problem solving and basic math skills that I will undoubtedly be exposed to in the world of medicine.

Doctors working in hospitals must constantly check on patients to ensure that they have the correct dosages of pharmaceuticals in their system as to make sure that medication administration will not be harmful. Wrong dosages can lead to permanent internal injury and, most traumatically, death. A more common and typical example of this is overdosing. In addition, doctors would be required to know the ratios of height, weight, and BMI of their patients and how these numbers would correlate to certain dosages.
Besides drugs in medicine, calculus can also be applied to being able to predict the amount of supplies it needs to sustain the hospital or clinic. This could be done by looking at graphs from previous years of how much each item was used and coming up with a relative equation that reflects the amount of supply from previous years. For example, an organ donation center would need to be able to calculate a certain quota for a hospital and make a reasonable estimate of how many of each organ they could possibly need for the future. Being able to interpret and make predictions about these numbers is derived from calculus.
In addition to its practical applications in a medical workplace, the problem solving and logistical skills gained by studying calculus are immediately transferrable to any medical career. As we know, both medicine and calculus require a great deal of familiarity of numbers and problem solving. However, the more calculus is studied, the idea of finding different ways to figure out problems becomes increasingly prominent. Since the medical field can potentially be very unpredictable, it is imperative that doctors are able to think quickly on their feet while simultaneously ensuring that the vital signs of the patients are stable. Heart rate, blood pressure, metabolic rate, and respiratory rate are all important and are identified in the medical world by numbers. For example, blood pressure is represented by systolic pressure over diastolic pressure. In other words, the highest pressure within the blood stream during the time the heart beats over the lowest pressure occurring between heartbeats - in “doctor talk” 120/80 mmHg. Numbers like these are important to recognize because it clarifies the difference between a normal blood pressure and one that is indicative of dangerous hypertension.
By having this basis of calculus in medicine, problem solving skills and the ability to interpret numbers are sharpened and will be extremely useful in this field. Whether we like it or not, the world is surrounded by math, and could not function without it.

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called "La geometrie."

Works Cited: http://plato.stanford.edu/entries/descartes/

User:ShaunaMaty

2011-01-28T05:27:26Z

ShaunaMaty: paper about calculus

''Calculus in Medicine''
In the future, I would like to continue my studies in order to pursue a career in the medical field. Regardless of what component I decide to specialize in, a good basis of calculus will guide me in many facets of this field because of the underlying lessons that come from studying calculus. While calculus is mainly about solving problems, the intrinsic lessons it teaches are a good preparation for the copious amount of problem solving and basic math skills that I will undoubtedly be exposed to in the world of medicine.

Doctors working in hospitals must constantly check on patients to ensure that they have the correct dosages of pharmaceuticals in their system as to make sure that medication administration will not be harmful. Wrong dosages can lead to permanent internal injury and, most traumatically, death. A more common and typical example of this is overdosing. In addition, doctors would be required to know the ratios of height, weight, and BMI of their patients and how these numbers would correlate to certain dosages.
Besides drugs in medicine, calculus can also be applied to being able to predict the amount of supplies it needs to sustain the hospital or clinic. This could be done by looking at graphs from previous years of how much each item was used and coming up with a relative equation that reflects the amount of supply from previous years. For example, an organ donation center would need to be able to calculate a certain quota for a hospital and make a reasonable estimate of how many of each organ they could possibly need for the future. Being able to interpret and make predictions about these numbers is derived from calculus.
In addition to its practical applications in a medical workplace, the problem solving and logistical skills gained by studying calculus are immediately transferrable to any medical career. As we know, both medicine and calculus require a great deal of familiarity of numbers and problem solving. However, the more calculus is studied, the idea of finding different ways to figure out problems becomes increasingly prominent. Since the medical field can potentially be very unpredictable, it is imperative that doctors are able to think quickly on their feet while simultaneously ensuring that the vital signs of the patients are stable. Heart rate, blood pressure, metabolic rate, and respiratory rate are all important and are identified in the medical world by numbers. For example, blood pressure is represented by systolic pressure over diastolic pressure. In other words, the highest pressure within the blood stream during the time the heart beats over the lowest pressure occurring between heartbeats - in “doctor talk” 120/80 mmHg. Numbers like these are important to recognize because it clarifies the difference between a normal blood pressure and one that is indicative of dangerous hypertension.
By having this basis of calculus in medicine, problem solving skills and the ability to interpret numbers are sharpened and will be extremely useful in this field. Whether we like it or not, the world is surrounded by math, and could not function without it.

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called "La geometrie."

Works Cited: http://plato.stanford.edu/entries/descartes/

Sandbox:DavidKohler/Schedule

2010-11-01T21:57:31Z

ShaunaMaty:

Simply write your name or student number next to an empty time slot that suits you. You're not allowed to move others of course. -- [[User:DavidKohler|DavidKohler]]

Tuesday November 2
* 3:00 - 3:20-Ghita Youssefi
* 3:20 - 3:40- Avi Harry
* 3:40 - 4:00-Albert Koenig
* 4:00 - 4:20
* 4:20 - 4:40
* 4:40 - 5:00

Wednesday November 3
* 9:20 - 9:40
* 9:40 - 10:00
* 10:00 - 10:20
* 10:20 - 10:40
* 10:40 - 11:00

Thursday November 4
* 2:40 - 3:00- Charly Huxford
* 3:00 - 3:20
* 3:20 - 3:40
* 3:40 - 4:00
* 4:00 - 4:20
* 4:20 - 4:40
* 4:40 - 5:00

Friday November 5
* 9:20 - 9:40- Sabrina Pannu
* 9:40 - 10:00- Shauna Maty
* 10:00 - 10:20
* 10:20 - 10:40
* 10:40 - 11:00

Course:MATH110/Archive/2010-2011/003/Groups/Group 01

2010-10-13T15:45:02Z

ShaunaMaty: /* Working on Solving Problems */

Group members:
* Catherine Chen
* Curtis Doucette
* Tanya Jacob
* Albert König
* Shauna Maty

----

== Deriving to the area of the pentagon using squares ==

[[File:P1120678.JPG]]

[[Media:P1120679.jpg]]

Unable to show steps on wiki. Hand written work will be submitted.

----

== Working on Solving Problems ==

1) There is no time difference! It is how the time has been written! One hour consists of 60 minutes. and When we add 20 minutes to this it adds up to 80 minutes bus drive. And this is the same exact amount that the driver needed for returning to the terminal

2) As the question is not saying at what time and at what place the policeman saw the woman, I conclude that the policeman was not there when the lady broke the law. The policeman only "might have" her driving. So she might be driving the right way at that time, but 5minues ago she was breaking the law in the absence of the law.
Another conclusion that can be made from this question is that the question is not including cars or any other types of vehicles that are related to an act of crime while driving. Hence we can also conclude that the woman must have been driving a bicycle instead of a car

3) The probability of labeling Apple and orange box correctly is 100% for people who know what an orange and what an apple looks like. But when we reach box three, it becomes tricky. The reason is that there are two different fruits inside of it and when we choose only one fruit, we will label that box according to the fruit picked. Hence the chance of saying the right name for the last box is 0. Because, if we pick an orange then we label the box as orange-box but in fact it is a orange-apple box. The same procedure happens when we pick apple from that box. The only chance of getting this right is to pick at least 3 different fruits from the third box and when we see that we have picked two different fruits we know that it is a combination.

4) If we look at brother in the first part of the sentence and then the plural form of brothers in the second half, we can easily say that this blind fiddler has only one brother.
Looking at it from another point we know that a fiddler is a person who cheats on people mainly for the sake of “robbing” their money. So we can look at this as a gang where one persons say that everyone in the organization is connected to the blind fiddler but none of us inside the organization are connected to each other. It looks like a pyramid, where the tip can be having multiple lines towards the bottom.

5) From different point of views there different numbers of rotationsa.

a)One way is when the picture on the coin is facing the same direction then it has revolved 2 times. One time at 0 degrees and one time at 180 degrees.

b)If we don’t care about the direction the coin’s picture is looking at we had a 360o rotation about its axis, which means that we had indefinite times of turn, until it reaches its origin.

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.
Let's say Reuben's birthday is on Dec 12, two days on Dec 10 he was 20 years old. On Dec 12 he is 21 years old. The next Dec12 he would be 22 years old. Later in Dec 13 the next year he would become 23 years old.

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. Based on how it is phrased, it has to be either the son or the daughter, because the mother and her OLDER brother are not the same age. Therefore, since the best and worst players are of opposite sex, this cannot be possible.

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.
Because it never specifies what intervals the trains come at, it could be the following: Brooklyn- 11:59, 12:09, 12:19 Bronx- 12:00, 12:10, 12:20. Based on when the man arrives at the train station, he could almost always end up picking Brooklyn because it departs 1 minute early.

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)?
Although it seems that it would just take 10 seconds for the clock to strike ten, simply double, this cannot be right because between 5 chimes, there is only 4 intervals of time so, letting C=chimes and I=intervals, it can be said that 5C+4I=5 and then the formula for the second one would be 10C+9I=x. So, each interval for the 5 chimes is equal to 5/4. Since there is 9 intervals when the clock strikes 10, you would have 5/4*9 which equals 11.25 therefore, it takes 11.25 seconds for the clock to strike ten.

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?
there are 6 ways that two of the four babies can be directly tagged. there is no way that three of the four babies can be directly tagged.

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?
No, you should not accept his bet. No matter how many red cards are in the first half, there has to be the exact same of black cards in the second half as there are red cards in the first half. A half of a deck totals to 26 cards and since there are two colors, red and black, the number of red and black cards will be mirrored oppositely. Example: if Alex splits the deck of cards, and we count what we have in the first half, say 20 black cards and 6 red cards, we know without looking that there are going to be 20 red and 6 black in the other half, simply because there are only 2 colors and 26+26=52

[['''Curtis: 16-20''']]

'''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?

'''First we must translate this information into an equation for the daughters and sons. Let S= sisters and let B= brothers then our equation for the daughters is: S-1=B, and for the sons is: S=2(B-1) Next we solve for B by substituting the information we have that S=B+1: B+1=2(B-1), 1=2B-2-B, 3=2B-B, B=3 therefore by substituting B=3 into S-1=B we get: S-1=3 so S=4. We can then see that there are 4 sisters and 3 brothers.'''

'''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.

'''Again, we start with equations. Let D= Dan's weight, let S= Sarah's weight and let x= the amount the scale is off by. Then our equations will be D+x=60, S+x=50, and D+S+x=105. Then we can do some simple algebra and substitution to get D=60-x, S=50-x, and (60-x)+(50-x)+x=105. Finally, we can solve for x: -2x+x=105-60-50, -x=-5, x=5. So, the scale is adding 5 kilograms.'''

'''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?

'''This time we can simply write an equation for the problem letting x= the number of pennies in the jar: 2(2(2x/3)/3)/3=40 and then by reversing this operation we get: x=3(3(3(40)/2)/2)/2 which is really terrible to look at so it can also be viewed as x=40(3/2)^3 therefore x=135. The number of pennies that was in the jar to begin with is 135.'''

'''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?

'''Once more, you guessed it! We are going to write an equation. Let M= total milk consumed by Angela's family in the morning and C= total coffee consumed by Angela's family in the morning and x= the number of members in Angela's family. Our equation will be (M/4 + C/6)x= M+C. Regrouping, we get 2C(6-x)=3M(x-4). Since both C and M are positive quantities, both (6-x), and (x-4) are also positive, which is only possible when x = 5. Therefore, Anglela's family has 5 members in it.
'''

'''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?

'''This one is pretty easy since every hour each clock moves 5 minutes away from the other. ie the gap between them is increased by 10 minutes each hour. 60(minutes in an hour)/10(minutes clocks move apart)=6 so, after 6 hours the clocks will be an hour apart. Therefore, the clocks will be 6 hours apart at 6 am.'''

21. Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

Sven is the median of the sequence. Dan is the 10th and Lars is the 16th, so there must be at least 16 runners in order to have a 16th placement. Since 16 is an even number the isn't an exact median in the sequence. So 17, the next number would be reasonable. The median would be 9. Sven is placed exactly the 9th, which is the middle among all 17 runners, faster than Dan and Lars.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

It is impossible to determine the ages of Paula's children. The first piece of information only gives possible combinations that adds up/ multiplies up to 36. We don't know the date of today, we only know that the sum cannot be larger than 31, and their ages has to be smaller than 10 for each child because their product cannot exceed 36.
The second piece of information
24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Let the length of the candle be 12cm. For the candle that takes 6 hours to burn out, we call it (a), for the other that takes 4 hours to burn out, we call it (b). With the length of 12 cm, we can calculate the rate of burning. For (a), the rate is 2cm/hr, for (b), the rate is 4cm/hr.

After an hour, (a) would be 10cm while (b) would be 8cm. After two hours, (a) would then be 8cm while (b) would be 4cm. This is when the length are exactly twice. So it takes two hours to have one candle exactly twice as long as the other candle.
[[Link title]]

Course:MATH110/Archive/2010-2011/003/Groups/Group 01

2010-10-13T15:40:45Z

ShaunaMaty: /* Working on Solving Problems */

Group members:
* Catherine Chen
* Curtis Doucette
* Tanya Jacob
* Albert König
* Shauna Maty

----

== Deriving to the area of the pentagon using squares ==

[[File:P1120678.JPG]]

[[Media:P1120679.jpg]]

Unable to show steps on wiki. Hand written work will be submitted.

----

== Working on Solving Problems ==

1) There is no time difference! It is how the time has been written! One hour consists of 60 minutes. and When we add 20 minutes to this it adds up to 80 minutes bus drive. And this is the same exact amount that the driver needed for returning to the terminal

2) As the question is not saying at what time and at what place the policeman saw the woman, I conclude that the policeman was not there when the lady broke the law. The policeman only "might have" her driving. So she might be driving the right way at that time, but 5minues ago she was breaking the law in the absence of the law.
Another conclusion that can be made from this question is that the question is not including cars or any other types of vehicles that are related to an act of crime while driving. Hence we can also conclude that the woman must have been driving a bicycle instead of a car

3) The probability of labeling Apple and orange box correctly is 100% for people who know what an orange and what an apple looks like. But when we reach box three, it becomes tricky. The reason is that there are two different fruits inside of it and when we choose only one fruit, we will label that box according to the fruit picked. Hence the chance of saying the right name for the last box is 0. Because, if we pick an orange then we label the box as orange-box but in fact it is a orange-apple box. The same procedure happens when we pick apple from that box. The only chance of getting this right is to pick at least 3 different fruits from the third box and when we see that we have picked two different fruits we know that it is a combination.

4) If we look at brother in the first part of the sentence and then the plural form of brothers in the second half, we can easily say that this blind fiddler has only one brother.
Looking at it from another point we know that a fiddler is a person who cheats on people mainly for the sake of “robbing” their money. So we can look at this as a gang where one persons say that everyone in the organization is connected to the blind fiddler but none of us inside the organization are connected to each other. It looks like a pyramid, where the tip can be having multiple lines towards the bottom.

5) From different point of views there different numbers of rotationsa.

a)One way is when the picture on the coin is facing the same direction then it has revolved 2 times. One time at 0 degrees and one time at 180 degrees.

b)If we don’t care about the direction the coin’s picture is looking at we had a 360o rotation about its axis, which means that we had indefinite times of turn, until it reaches its origin.

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.
Let's say Reuben's birthday is on Dec 12, two days on Dec 10 he was 20 years old. On Dec 12 he is 21 years old. The next Dec12 he would be 22 years old. Later in Dec 13 the next year he would become 23 years old.

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. Based on how it is phrased, it has to be either the son or the daughter, because the mother and her OLDER brother are not the same age. Therefore, since the best and worst players are of opposite sex, this cannot be possible.

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.
Because it never specifies what intervals the trains come at, it could be the following: Brooklyn- 11:59, 12:09, 12:19 Bronx- 12:00, 12:10, 12:20. Based on when the man arrives at the train station, he could almost always end up picking Brooklyn because it departs 1 minute early.

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)?
Although it seems that it would just take 10 seconds for the clock to strike ten, simply double, this cannot be right because between 5 chimes, there is only 4 intervals of time so, letting C=chimes and I=intervals, it can be said that 5C+4I=5 and then the formula for the second one would be 10C+9I=x....

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?
there are 6 ways that two of the four babies can be directly tagged. there is no way that three of the four babies can be directly tagged.

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?
No, you should not accept his bet. No matter how many red cards are in the first half, there has to be the exact same of black cards in the second half as there are red cards in the first half. A half of a deck totals to 26 cards and since there are two colors, red and black, the number of red and black cards will be mirrored oppositely. Example: if Alex splits the deck of cards, and we count what we have in the first half, say 20 black cards and 6 red cards, we know without looking that there are going to be 20 red and 6 black in the other half, simply because there are only 2 colors and 26+26=52

[['''Curtis: 16-20''']]

'''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?

'''First we must translate this information into an equation for the daughters and sons. Let S= sisters and let B= brothers then our equation for the daughters is: S-1=B, and for the sons is: S=2(B-1) Next we solve for B by substituting the information we have that S=B+1: B+1=2(B-1), 1=2B-2-B, 3=2B-B, B=3 therefore by substituting B=3 into S-1=B we get: S-1=3 so S=4. We can then see that there are 4 sisters and 3 brothers.'''

'''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.

'''Again, we start with equations. Let D= Dan's weight, let S= Sarah's weight and let x= the amount the scale is off by. Then our equations will be D+x=60, S+x=50, and D+S+x=105. Then we can do some simple algebra and substitution to get D=60-x, S=50-x, and (60-x)+(50-x)+x=105. Finally, we can solve for x: -2x+x=105-60-50, -x=-5, x=5. So, the scale is adding 5 kilograms.'''

'''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?

'''This time we can simply write an equation for the problem letting x= the number of pennies in the jar: 2(2(2x/3)/3)/3=40 and then by reversing this operation we get: x=3(3(3(40)/2)/2)/2 which is really terrible to look at so it can also be viewed as x=40(3/2)^3 therefore x=135. The number of pennies that was in the jar to begin with is 135.'''

'''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?

'''Once more, you guessed it! We are going to write an equation. Let M= total milk consumed by Angela's family in the morning and C= total coffee consumed by Angela's family in the morning and x= the number of members in Angela's family. Our equation will be (M/4 + C/6)x= M+C. Regrouping, we get 2C(6-x)=3M(x-4). Since both C and M are positive quantities, both (6-x), and (x-4) are also positive, which is only possible when x = 5. Therefore, Anglela's family has 5 members in it.
'''

'''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?

'''This one is pretty easy since every hour each clock moves 5 minutes away from the other. ie the gap between them is increased by 10 minutes each hour. 60(minutes in an hour)/10(minutes clocks move apart)=6 so, after 6 hours the clocks will be an hour apart. Therefore, the clocks will be 6 hours apart at 6 am.'''

21. Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

Sven is the median of the sequence. Dan is the 10th and Lars is the 16th, so there must be at least 16 runners in order to have a 16th placement. Since 16 is an even number the isn't an exact median in the sequence. So 17, the next number would be reasonable. The median would be 9. Sven is placed exactly the 9th, which is the middle among all 17 runners, faster than Dan and Lars.

23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

It is impossible to determine the ages of Paula's children. The first piece of information only gives possible combinations that adds up/ multiplies up to 36. We don't know the date of today, we only know that the sum cannot be larger than 31, and their ages has to be smaller than 10 for each child because their product cannot exceed 36.
The second piece of information
24. Two candles of equal length were lit at the same time. One candle took 6 hr to burn out and the other candle took 3 hr to burn out. After how much time was one candle exactly twice as long as the other candle?

Let the length of the candle be 12cm. For the candle that takes 6 hours to burn out, we call it (a), for the other that takes 4 hours to burn out, we call it (b). With the length of 12 cm, we can calculate the rate of burning. For (a), the rate is 2cm/hr, for (b), the rate is 4cm/hr.

After an hour, (a) would be 10cm while (b) would be 8cm. After two hours, (a) would then be 8cm while (b) would be 4cm. This is when the length are exactly twice. So it takes two hours to have one candle exactly twice as long as the other candle.
[[Link title]]

Course:MATH110/Archive/2010-2011/003/Groups/Group 01

2010-10-13T07:21:17Z

ShaunaMaty: /* Working on Solving Problems */

User:ShaunaMaty

2010-09-19T20:56:19Z

ShaunaMaty:

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called "La geometrie."

Works Cited: http://plato.stanford.edu/entries/descartes/

User:ShaunaMaty

2010-09-19T20:56:03Z

ShaunaMaty:

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called "La geometrie".

Works Cited: http://plato.stanford.edu/entries/descartes/

User:ShaunaMaty

2010-09-19T20:55:15Z

ShaunaMaty:

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called La geometrie.

Works Cited: http://plato.stanford.edu/entries/descartes/

User:ShaunaMaty

2010-09-19T20:54:25Z

ShaunaMaty: Info and Essay

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called La geometrie.

Works Cited: http://plato.stanford.edu/entries/descartes/

User:ShaunaMaty

2010-09-19T20:51:29Z

ShaunaMaty: Blanked the page

User:ShaunaMaty

2010-09-19T20:50:51Z

ShaunaMaty: Essay and Info

Hi everyone, my name is Shauna Maty and I am a first year student in the Faulty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called ''La geometrie''.

Works Cited:
http://plato.stanford.edu/entries/descartes/

User talk:ShaunaMaty

2010-09-19T20:39:27Z

ShaunaMaty: Essay on Descartes and Analytic Geometry

My name is Shauna Maty and I am a first year in the Faculty of Arts. I'm from Colorado and I play hockey.

Rene Descartes, a famous French mathematician, brought forth analytical geometry in 1637. Descartes’ discoveries within analytic geometry were a gateway to calculus and for other great discoveries by Sir Isaac Newton and G.W. Leibniz. Analytical geometry is a branch of geometry that involves using points in respect to a coordinate system; most commonly, the Cartesian coordinate system. In fact, this coordinate system which Descartes created still bears his name today. His method to his findings were primarily algebraic, leading to his discoveries in analytic geometry to help find distances, slopes, midpoints and other equations to help with reading graphs. Essentially, he is credited with having made the important connection of geometry and algebra: the solving of geometrical problems by way of algebraic equations. Descartes’ findings gave him the ability to seamlessly blend the analytical tools of algebra and the visual immediacy of geometry by conjuring up a way to actually visualize algebraic functions. His brilliant ideas were eventually published in 1637 in a treatise called'' La geometrie''.

Works Cited:
http://plato.stanford.edu/entries/descartes/