UBC Wiki - User contributions [en]

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

2011-02-04T07:36:50Z

AgnesLuong:

='''<big>Homework 13</big>'''=

Pick one of the topic offered below and then explain in your own words what it means that these concepts work on a logarithmic scale. Create a wiki page with all your explanations. The length of that page is up to you, but it should feel like the work of four people thinking about a topic and trying to make sense of it. If you drafted something and would like some comments (within 24 hours), send me an email and a link where to look at, I'll post comments).
Topics:
* Decibels
* Richter magnitude scale
* Brightness of stars
* pH

If you have another idea, please send me an email to confirm your choice of topic.

[[/Logarithmic scale/]]

'''Decibels'''

If say we are at a concert and we are standing near the speakers then obviously the sound that you hear would be very loud and thus the decibels would be very high. However the further and further you stand from the speakers the quieter the sound would seem, even at a concert.

Now assume that for every 2 meters away from the sound source you move the decibels decrease by one third, this then can be measured by a function with the base 1/3.

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

2011-02-04T04:48:01Z

AgnesLuong: /* Homework 13 */

User:AgnesLuong

2011-01-28T07:39:21Z

AgnesLuong:

Hello,

My name is Agnes. To prevent from boring you too much, I will refrain from going into too much detail about myself, thus ending my introduction here would be appropriate.

I have picked The Pythagorean Theorem as my topic. Whenever we hear the words "Pythagorean Theorem" we usually associate it with the equation a^2 + b^2 = c^2. This infamous theorem was first used by the Greek philosopher Pythagoras of Samos. This theorem can be used to find a side missing side of a right triangle if the other two sides are known. Pythagoras figured this through the use of triangles. I found the following video rather interesting:

http://www.youtube.com/watch?v=xLkfDdsnpuY&feature=player_embedded

Here, we can see how the third unknown side is figured out by the use of squares and why this theorem is only applicable to right triangles. This was even more impressive as back in the 900 BCE calculators, of course, did not exist and mathematicians back then could only rely on diagrams to produce their theorems.

'''Homework 12'''

Ever wondered why your fanny pack costs what it does? Due to our ever changing world the price of fanny packs changes as well. Calculus is used to measure the rate of change in a situation; this concept is most fitting to be applied to the change in prices of goods and services as studied in economics.

Economics is the study of production, distribution and consumptions of goods and services, thus prices can be calculated accordingly. An example would be a model describing supply and demand the marginal cost, or the cost it takes to make one more of the product can be calculated.
For instance a company makes a total of fifteen trillions of fanny packs to sell (because they are the most popular things in the world) they would be able to calculate the increase of cost per fanny pack that they would make. This is most important in economics because it is about producing as much as one can within their limits. Obviously any company would want to have profits from their products. Finding the marginal costs can allow the companies to find a base price to charge for their products.

Another factor affecting the price of goods on the market is the demand elasticity. What the demand elasticity does is that it adjusts the price of goods depending on how much it is sought after , such that one percent change in price can be calculated due to the change of the demand product. For example if all of a sudden fanny packs were no longer popular, then the demand elasticity may decrease by more than one percent because the want for the fanny packs amongst the population is not as high anymore.

However the price of those fanny packs are not only dependent on how much it costs to make one, and how much the population want s it, but also how much one can pay for it. In the income elasticity of demand calculates how much a product should be worth due to the incomes of the population with both being measured in percentages. This allows for goods to be sold at the price in which they are sold and also holds the selling price constant.

The study of economics is dependent on the measure of the rate of change, as different events occur in the world, either man-made or natural, it would affect the prices of certain goods and services. Calculus is vital in determining the prices of our favorite dolls, computers and other goods by measuring how much one wants, how much one is willing to pay and so on. Not only is it found in economics but in other areas as well such as the sciences and so on.

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

2010-12-02T07:06:35Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y

x < y

4. x is less than or equal to y

x <math>\leq</math> y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''

The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.

'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

if 2x <math>\geq</math> 5 <math>\longrightarrow</math> then to isolate x, divide both sides by 2

x <math>\geq</math> <math>\{5 \over 2}\</math>

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:59:53Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y

x < y

4. x is less than or equal to y

x <math>\leq</math> y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''

The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.

'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

if 2x <math>\geq</math> 5 <math>\longrightarrow</math> then to isolate x, divide both sides by 2

x <math>\geq</math> <math>\frac{5}{2}\</math>

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:59:06Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y

x < y

4. x is less than or equal to y

x <math>\leq</math> y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

if 2x <math>\geq</math> 5 <math>\longrightarrow</math> then to isolate x, divide both sides by 2

x <math>\geq</math> <math>\tfrac{5}{2}\</math>

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:57:09Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y

x < y

4. x is less than or equal to y

x <math>\leq</math> y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

if 2x <math>\geq</math> 5 <math>\longrightarrow</math> then to isolate x, divide both sides by 2

x <math>\geq</math> \tfrac{5}{2}

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:53:50Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y

x < y

4. x is less than or equal to y

x <math>\leq</math> y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:53:00Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

x <math>\geq</math> y

3. x is less than y
x < y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:52:41Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is greater than or equal to y

<math>\geq</math>

3. x is less than y
x < y

5. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:50:33Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is less than y
x < y

3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''

[http://www.purplemath.com/modules/ineqgrph.htm] Written step-by-step explanation

[http://www.youtube.com/watch?v=0X-bMeIN53I] Video Explanation

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

2010-12-02T06:49:50Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is less than y
x < y

3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

'''Online References/extension'''
[http://www.purplemath.com/modules/ineqgrph.htm]

[http://www.youtube.com/watch?v=0X-bMeIN53I]

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

2010-12-02T05:55:36Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is less than y
x < y

3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

Solve it like a linear equation.

'''Goal''': to isolate the variable so that you can determine the interval of "x"

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to solving addition/subtraction equations

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

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

2010-12-02T05:49:54Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y" which can be written as

x>y.

2. x is less than y
x < y

3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to the addition

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

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

2010-12-02T05:49:30Z

AgnesLuong:

'''What is an inequality?'''

It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".

1. It may be that "x" is greater than "y"
which can be written as x>y.

2. x is less than y
x < y

3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation ('''such as the notation used for defining a domain'''), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to the addition

'''How to solve quadratic inequalities?'''

Let us look at an example of a quadratic inequality:

-x2 + 9 < 0

Our first step is to associate this with and equation. Therefore:

y= -x2 + 9

The next step is to find out where the equation cuts the graph on the x-axis. This means equating it to 0

-x2 + 9 = 0

Now we can solve:

-x2 + 9 = 0

x2 + 9 = 0

(x+3) (x-3) = 0

x=-3 x=3 Now we know that our quadratic equation crosses the x-axis at these values

We now get 3 different intervals at the points where the x-axis is cut

1.) x < -3

2.) -3 < x < 3

3.) x > 3

The next step is to find out on which intervals is the graph below the x-axis. In order to do this we must look at our original equation:

y = -x2 + 9 since it is a negative quadratic we can say that the graph would be facing down. Thus, in order to solve our original inequality of

-x2 + 9 < 0 we must look at where our y values are less than 0

From this we can see that the solution is: x < -2 or x > 2

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

2010-11-30T07:35:40Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation (such as the notation used for defining a domain), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>\infty</math>)

'''Multiplication/Division'''

is similar to the addition

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:35:06Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation (such as the notation used for defining a domain), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>infty</math>)

'''Multiplication/Division'''

is similar to the addition

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:33:18Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

They can be represented in an interval notation (such as the notation used for defining a domain), as it specifies what group of number that fits under this rule.

'''How to solve linear inequalities?'''

'''Addition/Subtraction'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

In this example "x" can be any number grater than two, and thus can be written like this (2,<math>inf</math>

'''Multiplication/Division'''

is similar to the addition

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:19:27Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign

x + 8 = 10 <math>\longrightarrow</math> isolate the variable

x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign

x > 2

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:19:07Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10 <math>\longrightarrow</math> substitute the = sign
x + 8 = 10 <math>\longrightarrow</math> isolate the variable
x = 2 <math>\longrightarrow</math> replace the equal sign with the original inequality sign
x > 2

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:08:08Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''
The equation can be seen as a normal equation, instead of the greater than, less than, not equal to sign, just let the = sign replace them for now.
Then solve the equation algebraically, afterwards substitute the equations' original inequality sign.
'''EX'''

x + 8 > 10<math>\longrightarrow</math>

'''How to solve quadratic inequalities?'''

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

2010-11-30T07:00:46Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>\neq;</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''
The equation can be seen as

'''How to solve quadratic inequalities?'''

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

2010-11-30T06:48:08Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>≠</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''

'''How to solve quadratic inequalities?'''

The equation can be seen as

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

2010-11-30T06:47:36Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math> &ne </math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''

'''How to solve quadratic inequalities?'''

The equation can be seen as

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

2010-11-30T06:47:07Z

AgnesLuong:

'''What is an inequality?'''
It is exactly what it sounds, it's definition is that two numbers are not equal to each other. Such as "y" is not equal to "x".
1. It may be that "x" is greater than "y"
which can be written as x>y.
2. x is less than y
x < y
3. x is not equal to y

x <math>&ne</math> y

'''How to represent the solutions of inequalities?'''

'''How to solve linear inequalities?'''
'''Addition'''

'''How to solve quadratic inequalities?'''

The equation can be seen as

Sandbox:DavidKohler/Schedule

2010-11-02T01:48:35Z

AgnesLuong:

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 Gracie Mann
* 9:40 - 10:00
* 10:00 - 10:20 Agnes Luong
* 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 10/Homework 4

2010-10-19T06:53:40Z

AgnesLuong:

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

Let C= Carla, P= Petra, J=Janet, S=Sandra, L=Li and F= Fernanda
The first match is CP but at the same time it is possible for JS, JF/LS, LF/ FS to have a match, let's assume JS and LF are playing against each other here.
The second match consists of CJ and a possibility of the following pairings PL, PF/ LS,/ and FS.
We assume that PL and FS play simultaneous to CJ.
The third match is J against L, while the possible matches are PS, PF/ CS we assume that PF and CS play against each other.
The fourth match is P against S and the possible matches at the same time are CL and JF.
By the fifth match only Carla is left who has not played against Fernanda.

'''5. Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

During the 9 days of vacation, Homer will be able to sleep on Tuesday. In order to have come to this answer the problem must have been analysed. Based on the problem given we can immediately rule out the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This is because Homer is waken in all of these days. This leaves us with the Tuesday,Thursday and Friday however the problem also mentions that none of the noisemakers was quiet for three consecutive days and no pair made noise on more than one day. Looking at this we can slowly rule out each noisemaker based on which days they have already waken Homer. The construction workers would have waken Homer up on Thursday since none were quiet for three straight days while the Dog may have waken Homer on either Thursday,Friday or Saturday. This leaves us with the Salesman who must have waken Homer up on Friday since, like the other noisemakers it cannot be silent for 3 consecutive days. This leaves Tuesday free of any obstructions.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10/Homework 4

2010-10-19T06:48:22Z

AgnesLuong:

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

Let C= Carla

'''5. Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

During the 9 days of vacation, Homer will be able to sleep on Tuesday. In order to have come to this answer the problem must have been analysed. Based on the problem given we can immediately rule out the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This is because Homer is waken in all of these days. This leaves us with the Tuesday,Thursday and Friday however the problem also mentions that none of the noisemakers was quiet for three consecutive days and no pair made noise on more than one day. Looking at this we can slowly rule out each noisemaker based on which days they have already waken Homer. The construction workers would have waken Homer up on Thursday since none were quiet for three straight days while the Dog may have waken Homer on either Thursday,Friday or Saturday. This leaves us with the Salesman who must have waken Homer up on Friday since, like the other noisemakers it cannot be silent for 3 consecutive days. This leaves Tuesday free of any obstructions.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10/Homework 4

2010-10-19T06:48:04Z

AgnesLuong:

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

'''5. Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

During the 9 days of vacation, Homer will be able to sleep on Tuesday. In order to have come to this answer the problem must have been analysed. Based on the problem given we can immediately rule out the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This is because Homer is waken in all of these days. This leaves us with the Tuesday,Thursday and Friday however the problem also mentions that none of the noisemakers was quiet for three consecutive days and no pair made noise on more than one day. Looking at this we can slowly rule out each noisemaker based on which days they have already waken Homer. The construction workers would have waken Homer up on Thursday since none were quiet for three straight days while the Dog may have waken Homer on either Thursday,Friday or Saturday. This leaves us with the Salesman who must have waken Homer up on Friday since, like the other noisemakers it cannot be silent for 3 consecutive days. This leaves Tuesday free of any obstructions.

Course:MATH110/Archive/2010-2011/003/Groups/Group 10/Homework 4

2010-10-19T06:18:49Z

AgnesLuong:

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

Since all the players play against another only once, on the fifth day it is possible that any of the players would play against Fernanda as she has not played against any of the players yet.

'''5. Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

During the 9 days of vacation, Homer will be able to sleep on Tuesday. In order to have come to this answer the problem must have been analysed. Based on the problem given we can immediately rule out the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This is because Homer is waken in all of these days. This leaves us with the Tuesday,Thursday and Friday however the problem also mentions that none of the noisemakers was quiet for three consecutive days and no pair made noise on more than one day. Looking at this we can slowly rule out each noisemaker based on which days they have already waken Homer. The construction workers would have waken Homer up on Thursday since none were quiet for three straight days while the Dog may have waken Homer on either Thursday,Friday or Saturday. This leaves us with the Salesman who must have waken Homer up on Friday since, like the other noisemakers it cannot be silent for 3 consecutive days. This leaves Tuesday free of any obstructions.

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

2010-10-13T05:57:50Z

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

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.

'''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.

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

2010-10-13T05:48:18Z

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

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.

'''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.

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

2010-10-13T05:41:57Z

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

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.

'''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 a pair had to be drawn consecutively, there is a possibility that that may never happen

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

2010-10-13T05:22:14Z

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

User:AgnesLuong

2010-09-20T01:20:25Z

AgnesLuong:

User:AgnesLuong

2010-09-20T01:13:29Z

AgnesLuong:

User:AgnesLuong

2010-09-18T21:07:31Z

AgnesLuong: Created page with 'Hello, My name is Agnes. The interesting thing about me is that I am not interesting at all. This is my first year at UBC.'

Hello,

My name is Agnes. The interesting thing about me is that I am not interesting at all. This is my first year at UBC.