how to prove this?? The sum can be carried out with the help of the standard...
Show that a spontaneous chemical process that is carried out in a closed system at constant S and P is driven by a decrease in enthalpy. Please help. Thank you! how that a spontaneous chemical process that is carried out in a closed system at con- stant S and P is driven by a decrease in enthalpy. Hint: Start with the fundamental equation for dH and note that Σ μǐdNF SVVNs then use the rectified form of the Clausius inequality.
A study was carried out to find when people show up to parties-how late is fashionably late? We asked hosts to record, either by stopwatch or sign-in, when guests arrived. We got detailed data from many parties held last year. The parties vary in size, ranging from small family dinner parties to large end-of- year celebrations. The following is a scatter plot of median arrival time (measured in minutes) against number of guests at each party. The incomplete output for...
Once again, you can easily use induction to prove the very cool fact that the sum of the first n perfect cubes is equal to the square of the nth triangular number, but can you do it with a picture, instead? 2.4.8 Once again, you can easily use induction to prove the very cool fact that the sum of the first n perfect cubes is equal to the square of the nth triangular number, but can you do it with...
b. State the Leibnitz formula for determinants and describe how to get for an n × n-matrix nt-many terms. Explain how for a triangular matrix only one term can be non-zero. 10. State and prove Cramer's rule. b. State the Leibnitz formula for determinants and describe how to get for an n × n-matrix nt-many terms. Explain how for a triangular matrix only one term can be non-zero. 10. State and prove Cramer's rule.
PROOFS: Use these theorems and others to prove these statements. Theorem 1: The sum of two rational numbers is rational. Theorem 2: The product of two rational numbers is rational. Theorem 3: √ 2 is irrational. Induction: Prove that 6 divides n 3 − n for any n ≥ 0 Use strong induction to prove that every positive integer n can be written as the sum of distinct powers of 2. That is, prove that there exists a set of...
Prove that Box-Muller method described in class generates independent standard normal random variables. 4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n to write a function which wi σ-) random variables b) Suppose that X is an exponential random variable with rate parameter λ and that Y is the integer part of X. Show that Y has a geometric distribution and use this result to give an algorithm to generate a random sample...
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...
(b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and je[1,2,..., n) then sin2 (2ntj/n) = n/2 t-1 so long as jメ1n/21, where Ir] is the greatest integer that is smaller than or equal to x. We were unable to transcribe this image (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer...
Can someone answer number 4 for me? (60 pt., 12 pt. each) Prove each of the following statements using induction. For each statement, answer the following questions. a. (2 pt.) Complete the basis step of the proof b. (2 pt.) What is the inductive hypothesis? c. (2 pt.) What do you need to show in the inductive step of the proof? d. (6 pt.) Complete the inductive step of the proof. 1. Prove that Σ(-1). 2"+1-2-1) for any nonnegative integer...
14) (15 pts) Show how the following synthetic conversion can be carried out. In addition to the material given, you may use any needed solvents, inorganic reagents, and organic compounds with fhree or fewer carbons. If needed, use the back of this page to give your answer OH NO2