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3. Consecutive Sums a. (4 pts) Write 90 as the sum of consecutive positive integers in as many wa...
What is the smallest positive integer that can be expressed as the sum of nine consecutive positive integers, the sum of ten consecutive positive integers, and the sum of eleven consecutive positive integers
What is the smallest positive integer that can be expressed as the sum of nine consecutive positive integers, the sum of ten consecutive positive integers, and the sum of eleven consecutive positive integers? Explain how you arrived at this number.
For Exercises 1-15, prove or disprove the given statement. 1. The product of any three consecutive...
For Exercises 1-15, prove or disprove the given
statement.
1. The product of any three consecutive integers is even.
2. The sum of any three consecutive integers is
even.
3. The product of an integer and its square is
even.
4. The sum of an integer and its cube is even.
5. Any positive integer can be written as the sum of
the squares of two integers.
6. For a positive integer
7. For every prime number n, n +...
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, whe...
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, where order does not matter. For example, two partitions of 7 are 7 1+1+1+4 and 7=1+1+1+2+2. A partition of n is perfect if every integer from 1 to n can be written uniquely as the sum of elements in the partition. 1+1+1+4 is perfect since 1-7 are expressed only as 1, 1+1, 1+1+1, 4, 1+4, 1+1+4 and 1+1+1+4, but 1+1+1+2+2...
use simple C++ please Exercise 3: Write a program that reads a positive number and checks...
use
simple C++ please
Exercise 3: Write a program that reads a positive number and checks if the number can be expressed as a sum of two prime numbers. If yes, write all possible ways of expressing the number as sum of primes. Note: n is a prime if it is divisible only by 1 and itself, hence not divisible by any integer in the range from 2 to sqrt(n), both inclusive. Write a function is Prime that take a...
1. (2 pts) Find the argument form for the following argument and determine whether it is...
1. (2 pts) Find the argument form for the following argument and determine whether it is valid. Can we conclude that the conclusion is true if the premises are true? If George does not have eight legs, then he is not a spider. George is a spider. .:. George has eight legs. 2. (2 pts) What rules of inference are used in this famous argument? "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." 3. (2 pts)...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving k...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving ku=(n)u The previous theorem not only asserts that an appropriate exponent is always availahle, but it also tells us how to find it. The numbers u and are solutions lo a lincar Diophantine cquation just like those we studied in Chapter 6.33 Exercisc. Use your observations so far to find solutions to the follow ing congruences. Be sure...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...
need question 3 assap using cin and cout outputs please Ctrl CSC 270 Final Exam-Spring2 1) [10 pts] Create anarray x which includes integers fron ltos obtain the array y which, even formula. Displ...
need question 3 assap using cin and cout outputs please
Ctrl CSC 270 Final Exam-Spring2 1) [10 pts] Create anarray x which includes integers fron ltos obtain the array y which, even formula. Display both arrays x and y in a table with labeled column headings. 0 y- 2x+1 2) 120 pts] Consider the following 2D array. 01 2 -1 X-3 5 0 6 -3 7 -15 Use the standard notation and obtain the following (a) Create and display array...
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
6. [10 pts] The table below gives the values of a function f(x, y) on the square region R-[0,4] x [0,4]. -2-4-3 You have to approximate f(r, y) dA using double Riemann sums. Riemann sum given (a)...
6. [10 pts] The table below gives the values of a function f(x, y) on the square region R-[0,4] x [0,4]. -2-4-3 You have to approximate f(r, y) dA using double Riemann sums. Riemann sum given (a) What is the smallest AA ArAy you can use for a double the table above? (b) Sketch R showing the subdivisions you found in part (a). (e) Give upper and lower estimates of y) dA using double Riemann sums with subdivisions you found...
For Exercises 1-15, prove or disprove the given
statement.
1. The product of any three consecutive integers is even.
2. The sum of any three consecutive integers is
even.
3. The product of an integer and its square is
even.
4. The sum of an integer and its cube is even.
5. Any positive integer can be written as the sum of
the squares of two integers.
6. For a positive integer
7. For every prime number n, n +...
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, where order does not matter. For example, two partitions of 7 are 7 1+1+1+4 and 7=1+1+1+2+2. A partition of n is perfect if every integer from 1 to n can be written uniquely as the sum of elements in the partition. 1+1+1+4 is perfect since 1-7 are expressed only as 1, 1+1, 1+1+1, 4, 1+4, 1+1+4 and 1+1+1+4, but 1+1+1+2+2...
use
simple C++ please
Exercise 3: Write a program that reads a positive number and checks if the number can be expressed as a sum of two prime numbers. If yes, write all possible ways of expressing the number as sum of primes. Note: n is a prime if it is divisible only by 1 and itself, hence not divisible by any integer in the range from 2 to sqrt(n), both inclusive. Write a function is Prime that take a...
1. (2 pts) Find the argument form for the following argument and determine whether it is valid. Can we conclude that the conclusion is true if the premises are true? If George does not have eight legs, then he is not a spider. George is a spider. .:. George has eight legs. 2. (2 pts) What rules of inference are used in this famous argument? "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." 3. (2 pts)...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving ku=(n)u The previous theorem not only asserts that an appropriate exponent is always availahle, but it also tells us how to find it. The numbers u and are solutions lo a lincar Diophantine cquation just like those we studied in Chapter 6.33 Exercisc. Use your observations so far to find solutions to the follow ing congruences. Be sure...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...
need question 3 assap using cin and cout outputs please
Ctrl CSC 270 Final Exam-Spring2 1) [10 pts] Create anarray x which includes integers fron ltos obtain the array y which, even formula. Display both arrays x and y in a table with labeled column headings. 0 y- 2x+1 2) 120 pts] Consider the following 2D array. 01 2 -1 X-3 5 0 6 -3 7 -15 Use the standard notation and obtain the following (a) Create and display array...
6. [10 pts] The table below gives the values of a function f(x, y) on the square region R-[0,4] x [0,4]. -2-4-3 You have to approximate f(r, y) dA using double Riemann sums. Riemann sum given (a) What is the smallest AA ArAy you can use for a double the table above? (b) Sketch R showing the subdivisions you found in part (a). (e) Give upper and lower estimates of y) dA using double Riemann sums with subdivisions you found...
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