Homework Answers
Add Answer to:
. Ars Magna 2. Determine a if (a, a+ 1,+ 2) is a Pythagorean triple. What...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The prec...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The preceding theorem lets us easily generale infinitely many Pythagorean triples, but, in fact, cvery primitive Pythagorean triple can be generated by chousing appropriale natural numbers s and and making the Pythagorean triple as described in the preceding thcorem. As a hint to the proof, we make a little observation. 8.6 Lemma. Let (a, b,e) be a primitive Pythagorean...
Discrete Structures class. An ordered triple of positive integers (a,b,c) is called a Pythagorean Triple if...
Discrete Structures class.
An ordered triple of positive integers (a,b,c) is called a
Pythagorean Triple if a^2 + b^2 = c^2. Prove that if m & n are
pos int....
2) (10 pts) An ordered triple of positive integers (a, b, c) is called a Pythagorean Triple if a² + b2 = c2. Prove that if m and n are positive integers with m > n, then (m? – nº, 2mn, m² + n°) is a Pythagorean triple. Use this...
Re doing. A Pythagorean triple is a set of integers (a, b, c) satisfying a2+bc2. Write pseudocode...
re doing. A Pythagorean triple is a set of integers (a, b, c) satisfying a2+bc2. Write pseudocode (or Matlab code) that will output the number of unique Pythagorean triples that satisfy c< 200. [Unique means that you should not count (a 3, b 4, c 5) and (a 4, b 3, c 5) as two different triples, for example]. Explain why your program will work. Imagine a square n x n matrix A with diagonal elements which we believe to...
Co 2. (10 points) Let (a, b, c) be a primitive Pythagorean triple. Prove that cis...
Co 2. (10 points) Let (a, b, c) be a primitive Pythagorean triple. Prove that cis of the form 4k1. a thec ( Rlats ie 2 2
please prove the theorems, thank you very much 8.21 Theorem. A natural numbern can be written...
please prove the theorems,
thank you very much
8.21 Theorem. A natural numbern can be written as a sum of two squares of natural numbers if and only if every prime congruent to 3 modulo 4 in the unique prime factorization of n occurs to an even power Pythagorean triples revisited We are now in a position to describe the possible values for the hypotenuse in a primitive Pythagorean triple. 8.22 Theorem. If (a, h, e) is a primitive Pythagorean...
2. The triple (a, b, c) is called a Pythagorean triple if a, b and c...
2. The triple (a, b, c) is called a Pythagorean triple if a, b and c are natural numbers (in other words, they belong to N) and a2 +bc2. Prove that if a rectangle has sides of rational lengths p and q then the length of its diagonal is irrational if and only if there is a natural number r such that (p,q,r) is a a Pythagorean triple. State clearly any theorem proved in class that you use.
14. More Work with Pythagorean Triples. In Exercise (13), we verified that each of the following...
14. More Work with Pythagorean Triples. In Exercise (13), we verified that each of the following triples of natural numbers are Pythagorean triples: • 3, 4, and 5 • 6, 8, and 10 • 8, 15, and 17 • 10, 24, and 26 . 12, 35, and 37 • 14, 48, and 50 (a) Focus on the least even natural number in each of these Pythagorean triples. Let n be this even number and find m so that n =...
8.20 Question. Which natural mumbers can be written as the sum of two squares of natural raumbers? State and prove the...
8.20 Question. Which natural mumbers can be written as the sum of two squares of natural raumbers? State and prove the mast general theorem possible about which natural numbers can be written as the sum of two suares of nutural numbers, and prove it. We give the most gencral result next. 8.21 Theorem. A natural number n can be written as a sum of two squares of natural mumbers if and only if every prime congruent to 3 modulo 4...
Please use only C language and NOT C++ or Java You are now allowed to use...
Please use only C language and NOT C++ or Java You are now allowed to use the following • for loops • math.h and pow() function • formatting float and double numbers • switch statements • getchar() function • ASCII chart • do…while loops • break and continue statements • Logical AND (&&), logical OR (||), logical NOT (!) operators Pythagorean triples are three positive integer numbers a, b, c that form the sides of a right triangle, such that...
Establish the identity. (1+2 cot?e)? -2 cot?e+1 csc e-cote Use a Pythagorean identity to rewrite the...
Establish the identity. (1+2 cot?e)? -2 cot?e+1 csc e-cote Use a Pythagorean identity to rewrite the numerator in terms of csc and coto and factor the denominator into two factors by factoring the difference of two squ After cancelling common factors from the previous fraction, use a Pythagorean identity to rewrite the denominator. Write the new denominator below. The entire expression can now be rewritten as 2 cot?o + 1 using what? O A Quotient Identity O B. Even-Odd Identity...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The preceding theorem lets us easily generale infinitely many Pythagorean triples, but, in fact, cvery primitive Pythagorean triple can be generated by chousing appropriale natural numbers s and and making the Pythagorean triple as described in the preceding thcorem. As a hint to the proof, we make a little observation. 8.6 Lemma. Let (a, b,e) be a primitive Pythagorean...
Discrete Structures class.
An ordered triple of positive integers (a,b,c) is called a
Pythagorean Triple if a^2 + b^2 = c^2. Prove that if m & n are
pos int....
2) (10 pts) An ordered triple of positive integers (a, b, c) is called a Pythagorean Triple if a² + b2 = c2. Prove that if m and n are positive integers with m > n, then (m? – nº, 2mn, m² + n°) is a Pythagorean triple. Use this...
re doing. A Pythagorean triple is a set of integers (a, b, c) satisfying a2+bc2. Write pseudocode (or Matlab code) that will output the number of unique Pythagorean triples that satisfy c< 200. [Unique means that you should not count (a 3, b 4, c 5) and (a 4, b 3, c 5) as two different triples, for example]. Explain why your program will work. Imagine a square n x n matrix A with diagonal elements which we believe to...
Co 2. (10 points) Let (a, b, c) be a primitive Pythagorean triple. Prove that cis of the form 4k1. a thec ( Rlats ie 2 2
please prove the theorems,
thank you very much
8.21 Theorem. A natural numbern can be written as a sum of two squares of natural numbers if and only if every prime congruent to 3 modulo 4 in the unique prime factorization of n occurs to an even power Pythagorean triples revisited We are now in a position to describe the possible values for the hypotenuse in a primitive Pythagorean triple. 8.22 Theorem. If (a, h, e) is a primitive Pythagorean...
2. The triple (a, b, c) is called a Pythagorean triple if a, b and c are natural numbers (in other words, they belong to N) and a2 +bc2. Prove that if a rectangle has sides of rational lengths p and q then the length of its diagonal is irrational if and only if there is a natural number r such that (p,q,r) is a a Pythagorean triple. State clearly any theorem proved in class that you use.
14. More Work with Pythagorean Triples. In Exercise (13), we verified that each of the following triples of natural numbers are Pythagorean triples: • 3, 4, and 5 • 6, 8, and 10 • 8, 15, and 17 • 10, 24, and 26 . 12, 35, and 37 • 14, 48, and 50 (a) Focus on the least even natural number in each of these Pythagorean triples. Let n be this even number and find m so that n =...
8.20 Question. Which natural mumbers can be written as the sum of two squares of natural raumbers? State and prove the mast general theorem possible about which natural numbers can be written as the sum of two suares of nutural numbers, and prove it. We give the most gencral result next. 8.21 Theorem. A natural number n can be written as a sum of two squares of natural mumbers if and only if every prime congruent to 3 modulo 4...
Establish the identity. (1+2 cot?e)? -2 cot?e+1 csc e-cote Use a Pythagorean identity to rewrite the numerator in terms of csc and coto and factor the denominator into two factors by factoring the difference of two squ After cancelling common factors from the previous fraction, use a Pythagorean identity to rewrite the denominator. Write the new denominator below. The entire expression can now be rewritten as 2 cot?o + 1 using what? O A Quotient Identity O B. Even-Odd Identity...
Most questions answered within 3 hours.
-
With a $16 Trillion national ebt, and projected annual budget
eficits in excess of $1 Trillion...
asked 2 minutes ago -
A machine shop owner wishes to assign each of three machinists
(labeled 1, 2, and 3)...
asked 16 minutes ago -
Regarding language development, which of the following
statements is FALSE?
Babies are able to cry from...
asked 16 minutes ago -
A couple of small ice cubes at 0 °C are added to glass of warm
water...
asked 14 minutes ago -
Slow 'n Steady, Inc., has a stock price of $30, will pay a
dividend next year...
asked 17 minutes ago -
During the current financial year, the owner of Omega
Enterprises withdrew supplies of $2,000 for personal...
asked 13 minutes ago -
PLEASE SHOW MATH CALCULATION(formulas)it has to be done on excel
P12-4 Last year (2016), Richter Condos...
asked 22 minutes ago -
A 0.25μF capacitor is charged to 50 V . It is then connected in
series with...
asked 38 minutes ago -
Calculate the current, I, through the batteries for:
- a 2-bulb parallel circuit
- How does...
asked 39 minutes ago -
Choose the sentence that uses correct punctuation.
1a. The prefatory parts of a report include the...
asked 45 minutes ago -
For the element arsenic, which one of the following sets of
quantum numbers could not apply...
asked 55 minutes ago -
Compare and contrast the architectures of 3 types of ADCs:
Flash, SAR, and pipelined. Use the...
asked 56 minutes ago