Group 1
Write a C++ program or each of the following problems:
1. Write a C++ program to enter a distance in meters and print out its value in kilometers, yards, and miles. (Note: 1 m = 0.001 km = 1.094 yd = 0.0006215 mi). 2. Write a C++ program to enter length and width of a rectangle, compute and print the area and perimeter of the rectangle. Print both rounded to the nearest tenth of a foot. 3. Write a program to compute the cost for carpeting a room. Input should consist of the room length (in meters), room width (in meters), and carpet price per square meter. 4. Compute and print the number of minutes in a year.

5. Given a positive number, print its square and square root. 6. The arithmetic mean of two numbers is the result of dividing their some by 2. The geometric mean of two numbers is the square root of their product. The harmonic mean of two numbers is the arithmetic mean of their reciprocals. Write a program that takes two floating-point numbers as inputs and displays these three means. 7. Write a C++ program to take a depth (in kilometers) inside the earth as input data; compute and display the temperature at that depth in degrees Celsius and Fahrenheit. The relevant formulas are:

Celsius = 10 x (depth) + 20 (Celsius 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:

...The PythagoreanTheorem 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...

...PythagoreanTheorem
Diana Lorance
MAT126
Dan Urbanski
March 3, 2013
PythagoreanTheorem
In this paper we are going to look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagorean triples and asks if you can find more Pythagorean triples than the two that are listed which are (3,4, and 5) and (5,12, and 13) (Bluman, 2012). The...

...In mathematics, the Pythagoreantheorem — 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...

...PYTHAGOREANTHEOREM
More than 4000 years ago, the Babyloneans and the Chinese already knew that a triangle with the sides of 3, 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three, the second side four and the last side five sections long, they could easily construct a right angle.
A Greek scholar named Pythagoras, who...

...ancient Greek mathematician and philosopher. Pythagoras was responsible for important developments in the history of mathematics, astronomy, and the theory of music.
The thing that Pythagoras is probably the most famous for is the PythagoreanTheorem. The PythagoreanTheorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two...

...In mathematics, the PythagoreanTheorem — 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...

...THE WIZARD OF OZ 2
The Wizard of Oz
Scarecrow’s Speech on PythagoreanTheorem
The Pythagoreantheorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher, Pythagoras. In the Wizard of Oz, after the Scarecrow gets a brain, he states the Pythagoreantheorem. However, he...

...PythagoreanTheorem:
Some False Proofs
Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I'll list below some fallacious proofs of the Pythagoreantheorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion, a glaring error is committed in logic and leaves one wondering how it could have avoided being...

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