Week 4 Assignment
Shuna Tolbert
May 6, 2013
Week 4 Assignment
Mat126
Instructor Kussiy Alyass
Following completion of your readings, complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World.
Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.
After building your triples, verify each of them in the Pythagorean Theorem equation.
The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.
In this section we are learning about Pythagorean triples. A Pythagorean triple is a set of positive integers that fits the rule a2 + b2 = c2. In order to find a Pythagorean triple, the formula must be completed and the answer must turn out to be true. If not, then it will not be considered a Pythagorean triple and you will have to use different numbers until you find a set that makes up one.
Example 1: m = 3, n = 4 n² - m² = (4)² - (3)² = 16 - 9 = 7
2mn = 2(3)(4) = 24 n² + m² = (4)² + (3)² = 16 + 9 = 25
Triple: 7, 24, 25
Check:
(7)² + (24)² = (25)²
49 + 576 = 625 625 625
1. 7, 8
(8)2 - (7)2 = 64 – 48 = 15
2(7)(8) = 112
(8)2 + (7)2 = 64 + 49 = 113
Check:
(15)2 + (112)2 = (113)2
225 + 12544 = 12769
12769 = 12769
2. 5, 6
(6)2 – (5)2 = 36 – 25 = 11
2(5)(6) = 60
May 6, 2013
Week 4 Assignment
Mat126
Instructor Kussiy Alyass
Following completion of your readings, complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World.
Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.
After building your triples, verify each of them in the Pythagorean Theorem equation.
The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.
In this section we are learning about Pythagorean triples. A Pythagorean triple is a set of positive integers that fits the rule a2 + b2 = c2. In order to find a Pythagorean triple, the formula must be completed and the answer must turn out to be true. If not, then it will not be considered a Pythagorean triple and you will have to use different numbers until you find a set that makes up one.
Example 1: m = 3, n = 4 n² - m² = (4)² - (3)² = 16 - 9 = 7
2mn = 2(3)(4) = 24 n² + m² = (4)² + (3)² = 16 + 9 = 25
Triple: 7, 24, 25
Check:
(7)² + (24)² = (25)²
49 + 576 = 625 625 625
1. 7, 8
(8)2 - (7)2 = 64 – 48 = 15
2(7)(8) = 112
(8)2 + (7)2 = 64 + 49 = 113
Check:
(15)2 + (112)2 = (113)2
225 + 12544 = 12769
12769 = 12769
2. 5, 6
(6)2 – (5)2 = 36 – 25 = 11
2(5)(6) = 60