Reflection on Crib Bumpers
Tracey Crawford
ECE 214: Nutrition and Health of Children and Families
Kelly Wells
November 12, 2012

Kids in Danger website is value because it keeps parents as well as caregivers much needed information on recalls of certain things that are not safe for younger children. Kids in Danger website does have information on other website you can go to get more information about the product as well as numbers you can call. This website gave me a lot of information on crib bumpers pads and why they were recall. Due to an incident that happen in 2009 where 6-month-old Aiden died because of a crib bumper pad he rolled into and couldn’t get out. His grandmother who got kids in danger involved on the importance of crib safety and the danger of bumper pads told this story. We use this information by creating brochures or even books with activities that the parents as well as the caregivers to the safety on using products safe. We can even have seminars that would not cost too much for people to attend to give the importance on why certain toys and products have to be recall because more and more children are dying of things that can be prevented. We could also teach parents about how to use some of the product than just using what is read in the book because some of the products do come with instructions but people still could be putting it together wrong. If we educate more and more people on what is happening in the manufactures and why it happen than there would not be so much death. This information is essential to parents and caregivers on this information than there would not be so much deaths and serious injuries. I feel that parents need to know this information because if it were their own child or a family member they would want to know what they could do to prevent this from happening to them. I know we as people need to wake up and see what is going on in our neighborhoods as well as what...

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PythagoreanQuadratic
Member
MAT 222 Introduction to Algebra
Instructor Yvette Gonzalez-Smith
August 04, 2013
PythagoreanQuadratic
The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle, as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. It also can help a person to figure out whether or not the triangle is a right triangle or not, as long as the length of the other two sides are given (The Pythagorean Theorem, 1991-2012).
This week’s assignment was found on page 371; it is problem number 98, called “buried treasure”. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x+4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?
Although we were not given a direction for Ahmed’s half of the map, we figure that his and Vanessa’s paces will end up in the same place. I have drawn a diagram on a piece of scratch paper, which...

...Pythagorean Triples
Tammie Strohl
MAT 126
David Gualco
November 9, 2009
Pythagorean Triples
Pythagorean Theorem states that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest.
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If a, b, and c are positive integers, they are together called Pythagorean Triples.
The smallest such Pythagorean Triple is 3, 4 and 5. It can be seen that 32 + 42 = 52 (9+16=25).
Here are some examples:
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Endless
The set of Pythagorean Triples is endless.
It is easy to prove this with the help of the first Pythagorean triple, (3, 4, and 5):
Let n be any integer greater than 1: 3n, 4n and 5n would also be a set of Pythagorean triple. This is true because:
(3n)2 + (4n)2 = (5n)2
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So, you can make infinite triples just using the (3,4,5) triple.
Euclid's Proof that there are Infinitely Many Pythagorean Triples
However, Euclid used a different reasoning to prove the set of Pythagorean triples is unending.
The proof was based on the fact that the difference of the squares of any two consecutive numbers is always an odd number.
For example, 22 - 12 = 4-1 = 3, 152 - 142 = 225-196 = 29.
And also every odd number can be expressed as a difference of the squares of two consecutive numbers. Have a look at this table as an example:...

...The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length. Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea.
The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that:
"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
Figure 1
According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and...

...Historical Account:
Pythagoras, the namesake and supposed discoverer of the Pythagorean Theorem, was born on the Greek island of Samos in the early in the late 6th century. Not much is known about his early years of life, however, we do know that Pythagoras traveled through Egypt in the attempt to learn more about mathematics.
Besides his famous theorem, Pythagoras gained fame for founding a group, the Brotherhood of Pythagoreans, which was dedicated solely to study of mathematics and worship of numbers. Pythagoras passed on his belied that numbers are in fact the true "rulers of the universe".
While studying in Egypt, it is believed that Pythagoras studied with people known as the "rope-stretchers", the same people who engineered the pyramids. By using a special form of a rope tied in a circle with 12 evenly spaced knots, they discovered that if the rope was pegged to the ground in the dimensions of 3-4-5, the rope would create a right triangle. The rope stretchers used this principle to help accurately lay the foundations of for their buildings.
It was this fascination with the rope stretchers 3-4-5 triangle that ultimately led to the discovery of the Pythagorean theorem. While experimenting with this concept by drawing in the sand, Pythagoras found that if a square is drawn from each side of the 3-4-5 triangle, the area of the two smaller squares could be added together and equal the area of the large square....

...In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
The Pythagorean theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca. 495 BC), who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they used it in a mathematical framework.[4][5]
The theorem has numerous proofs, possibly the most of any mathematical theorem. These are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed,...

...Pythagorean Triples
Ashley Walker
MAT126
Bridget Simmons
November 28, 2011
A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (Bluman, 2005). A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer) (Vargas, 2008).
In project #4, pg. 522, (Mathematics in Our World) introduced some new information to add to my mathematics knowledge of numbers. The numbers 3, 4, and 5 are called Pythagorean triples since 32 + 42 = 52. The numbers 5, 12, and 13 are also Pythagorean triples since 52 + 122 = 132. Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples and write a brief report on the subject (Bluman, 2005).
When asked to find any other Pythagorean triples, I found 5, choosing 2 integers, m and n, with m less than n (Manuel, 2010). Three formulas I choose to form the Pythagorean triple, which can be calculated from:
n2 – m2
2mn
n2 + m2 (Manuel, 2010).
Project 4, pg.522
1) m=3, n=4
n2– m2=(4)2–(3)2=16-9=7 VERIFICATION:...

...temperature at depth in km)
Farhrenheit = 1.8 x (Celsius) + 32
8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example, if two sides of a right triangle have lengths 3 and 4, then the hypotenuse must have a length of 5. The integers 3, 4, and 5 together form a Pythagorean triple. There is an infinite number of such triples. Given two positive integers, m and n, where m > n, a Pythagorean triple can be generated by the following formulas:
Side1 = m2- n2
Side2 = 2mn
Hypotenuse = side12 + side22
Group 2
1. In a laboratory, the time of an experiment is measured in seconds. Write a C++ program to enter the time in seconds, convert and print out it as a number of hours, minutes and seconds. Use appropriate format for the output.
2. Write a C++ program to enter an integer number of 4 digits and print it out in an inverse order. For example if the input is 5723 the output should be 3275.
3. Draw a Flow chart and write a program in C++ that reads three integer numbers and computes their average. The program also determines the smallest number and prints out a message indicating whether that smallest number is even or odd. Print out the input and results with appropriate format.
4. Write a program that gets the coefficients of a quadratic equation ax2 + bx +...

...the nature of the roots of quadratics and cubic functions.
Part One
Case One
For Case One, the discriminant of the quadratic will always be equal to zero. This will result in the parabola cutting the axis once, or twice in the same place, creating a distinct root or two of the same root.
For PROOF 1, the equation y=a(x-b)2 is used.
PROOF 1
y = 3 (x – 2)2
= y = 3 (x2 – 4x + 4)
= y = 3x2 – 12x + 12
^ = b2 – 4ac
= (-12)2 – 4 x 3 x 12
= 144 – 144
= 0
The discriminant is equal to zero. The parabola touches the x-axis at (2, 0) and as a in the equation is a positive value, the parabola curves upwards.
For PROOF 2, the equation y=-a(x-b)2 is used.
PROOF 2
y = -3(x - 2)2
= y = -3 (x2- 4x + 4)
= y = -3x2 + 12x – 12
^ = b2 – 4ac
= 122 – 4 x (-3) x (-12)
= 144 – 144
= 0
The discriminant of the parabola is equal to zero. The parabola touches the x-axis at (2,0) and as a is a negative value, the parabola curves downwards.
For PROOF 3, the equation y=a(x-A)2 is used.
y = a (x – A)2
= y = a (x2 – 2Ax + A2)
= y = ax2 – 2aAx + aA2
^ = b2 – 4ac
= (- 2aA)2 – 4 x (a) x (aA2)
= 4a2A2 - 4a2A2
= 0
The discriminant of the parabola is equal to zero. The parabola touches the x- axis at (A, 0) and whether the parabola curves up or down is dependent on the whether A is a positive or negative value.
Case Two
In Case Two, the discriminant of the quadratic will be equal to a positive number....