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discrete math, use the the formula on the paper
m) (C5) How many integer solutions are...
Solve the equation. Give a general formula for all the solutions. List six solutions. Write the...
Solve the equation. Give a general formula for all the solutions. List six solutions. Write the general fomula for all the solutions to cosbased on the smaller angle. 8-□, k is any integer Simp y your answer Use angle measures greater than or equal to O and less than 2π ype an exact answer, using τ as needed. Use integers or ractions or any numbers in he expression. Type an expression using k as the variable. Write the general formula...
1. Fix n and k. How many positive integer solutions are there to x1 + +...
1. Fix n and k. How many positive integer solutions are there to x1 + + xk = n where xi i for all i?
8.3.47 Solve the equation. Give a general formula for all the solutions. List six solutions. 3...
8.3.47 Solve the equation. Give a general formula for all the solutions. List six solutions. 3 0 cos 2 2 0 3 based on the smaller angle Write the general formula for all the solutions to cos 2 0-k is any integer (Simplify your answer. Use angle measures greater than or equal to 0 and less than 2x Type an exact answer, using x as n- for any numbers in the expression. Type an expression using k as the variable.)...
Problem 3 Let n and k > l be positive integers. How many different integer solutions...
Problem 3 Let n and k > l be positive integers. How many different integer solutions are there to x1 +...+ In = k, with all xi <l?
Discrete math show all work please Use mathematical induction to prove that the statements are true...
Discrete math show all work please
Use mathematical induction to prove that the statements are true for every positive integer n. n[xn - (x - 2)] 1 + [x2 - (x - 1)] + [x:3 - (x - 1)] + ... + x n - (x - 1)] = 2 where x is any integer = 1
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
1. Let m be a nonnegative integer, and n a positive integer. Using the division algorithm...
1. Let m be a nonnegative integer, and n a positive integer. Using the division algorithm we can write m=qn+r, with 0 <r<n-1. As in class define (m,n) = {mc+ny: I,Y E Z} and S(..r) = {nu+ru: UV E Z}. Prove that (m,n) = S(n,r). (Remark: If we add to the definition of ged that gedan, 0) = god(0, n) = n, then this proves that ged(m, n) = ged(n,r). This result leads to a fast algorithm for computing ged(m,...
Problem 3. Let X and Y be two independent random variables taking nonnegative integer values (a)...
Problem 3. Let X and Y be two independent random variables taking nonnegative integer values (a) Prove that for any nonnegative integer m 7m k=0 b) Suppose that X~ B (n, p) and Y ~ B(m. p), and X, Y are independent. What is the distribution of the random variable Z X + Y? (c) Prove the following formula for binomial coefficients: n\ _n + m for kmin (m, n) (d) Let X ~ B (n, 1/2). What is P...
How many integer solutions are there for the inequality : x1 + x2 + x3 + x4 ≤ 15 (a) if xi ≥ 0 (b...
How many integer solutions are there for the inequality : x1 +
x2 + x3 + x4 ≤ 15
(a) if xi ≥ 0
(b) if 6 ≥ x1 ≥ 1, 6 ≥ x2 ≥ 1, x3 ≥ 0, x4 > 0
How many integer solutions are there for the inequality : x++ (a) if z 20
How many integer solutions are there for the inequality : x++ (a) if z 20
discrete math Search il 17:16 [Problem] 1 (a) Give an external definition of the set S {sls EZA+ and gcd(x, 12) 1) (...
discrete math
Search il 17:16 [Problem] 1 (a) Give an external definition of the set S {sls EZA+ and gcd(x, 12) 1) (B) Write all the proper subsets of the set {1, 2 3}, and (c) define the function for real number a and positive integer n ,f: RxZ^+ R as f (a,n) a^n , Give a recursive definition of the function (d) Calculate gcd (60, 22) using Euclidean algorithm (e) Give 3 positive integer x that satisfies 4x 6...
Solve the equation. Give a general formula for all the solutions. List six solutions. Write the general fomula for all the solutions to cosbased on the smaller angle. 8-□, k is any integer Simp y your answer Use angle measures greater than or equal to O and less than 2π ype an exact answer, using τ as needed. Use integers or ractions or any numbers in he expression. Type an expression using k as the variable. Write the general formula...
1. Fix n and k. How many positive integer solutions are there to x1 + + xk = n where xi i for all i?
8.3.47 Solve the equation. Give a general formula for all the solutions. List six solutions. 3 0 cos 2 2 0 3 based on the smaller angle Write the general formula for all the solutions to cos 2 0-k is any integer (Simplify your answer. Use angle measures greater than or equal to 0 and less than 2x Type an exact answer, using x as n- for any numbers in the expression. Type an expression using k as the variable.)...
Problem 3 Let n and k > l be positive integers. How many different integer solutions are there to x1 +...+ In = k, with all xi <l?
Discrete math show all work please
Use mathematical induction to prove that the statements are true for every positive integer n. n[xn - (x - 2)] 1 + [x2 - (x - 1)] + [x:3 - (x - 1)] + ... + x n - (x - 1)] = 2 where x is any integer = 1
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
1. Let m be a nonnegative integer, and n a positive integer. Using the division algorithm we can write m=qn+r, with 0 <r<n-1. As in class define (m,n) = {mc+ny: I,Y E Z} and S(..r) = {nu+ru: UV E Z}. Prove that (m,n) = S(n,r). (Remark: If we add to the definition of ged that gedan, 0) = god(0, n) = n, then this proves that ged(m, n) = ged(n,r). This result leads to a fast algorithm for computing ged(m,...
Problem 3. Let X and Y be two independent random variables taking nonnegative integer values (a) Prove that for any nonnegative integer m 7m k=0 b) Suppose that X~ B (n, p) and Y ~ B(m. p), and X, Y are independent. What is the distribution of the random variable Z X + Y? (c) Prove the following formula for binomial coefficients: n\ _n + m for kmin (m, n) (d) Let X ~ B (n, 1/2). What is P...
How many integer solutions are there for the inequality : x1 +
x2 + x3 + x4 ≤ 15
(a) if xi ≥ 0
(b) if 6 ≥ x1 ≥ 1, 6 ≥ x2 ≥ 1, x3 ≥ 0, x4 > 0
How many integer solutions are there for the inequality : x++ (a) if z 20
How many integer solutions are there for the inequality : x++ (a) if z 20
discrete math
Search il 17:16 [Problem] 1 (a) Give an external definition of the set S {sls EZA+ and gcd(x, 12) 1) (B) Write all the proper subsets of the set {1, 2 3}, and (c) define the function for real number a and positive integer n ,f: RxZ^+ R as f (a,n) a^n , Give a recursive definition of the function (d) Calculate gcd (60, 22) using Euclidean algorithm (e) Give 3 positive integer x that satisfies 4x 6...
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