\k – 1) (k) Show that some positive multiple of 51 has the last three digits...
Show that some positive multiple of 51 has the last three digits equal to 143.
The last three digits of my student id is 183
3) (30 pts) In this problem, the last two digits of your student number will be significant. Let N, be a number equal to the last digit of your student number, N, be a number equal to the last two digits of your student number. That is, if the last three digits of your student number is 83 then, N, = 3, N2 = 83. Consider a function f(x)=cos (11...
last three digits of ID: 523
College of Arts & Sciences Department of Chemistry & Earth Science جامة قطر GE Q2) (15 marks) A When phosphorus pentachloride, PCls, is heated at a constant pressure of exactly 1 bar to a temperature of 1400 K, the amount of phosphorus pentachloride decreases by X% (X: (last three digits of your st. QU ID)*0.02) because of dissociation to phosphorus trichloride, PCls, and chlorine, Clz. (a) Determine the equilibrium constant at this temperature. (b)...
A matrix A E Mnxn (F) is called nilpotent if, for some positive integer k, Ak O. A" O 1.Show that A eE Mnxn(F) is nilpotent the characteristic polynomial of A is t" 2. Show that if A, BE Mnxn(F) BA, then A + B is nilpotent. nilpotent and AB are 3. Show that if A, B e Mxn(F), A is nilpotent and AB BA, then AB is nilpotent. 4. If A E Mnxn(F) is nilpotent, find the inverse of...
E3. Show that Σ(-1)k( ) = 0 for all positive integers n and k with 0-k-n E4. Show that (t) = Σ ( . 71 に0 k+1 k"d) for all positive integers n and k with 0 ksn
10. Let dk -Ck*+1/2 exp(-k), where C is a strictly positive constant. At some point in the proof of Stirling's formula, we have that k! lim-= 1 and that (22n (n!)2 )2 (2nn+)2 (22n (dn)22 r π lim - Show that lim n→oo (dy.)"(2n+1) 2
10. Let dk -Ck*+1/2 exp(-k), where C is a strictly positive constant. At some point in the proof of Stirling's formula, we have that k! lim-= 1 and that (22n (n!)2 )2 (2nn+)2 (22n (dn)22...
PLEASE SHOW ALL STEPS WITH EXPLAINATION Let m and n be positive integers and let k be the least common multiple of m and n. Show that mZ∩nZ=kZ.
1. Multiple choice: Each question is worth 4 points (some useful equation are on last page) 1. As ionic strength increases, the values of activity coefficients: a. change randomly C. decrease b. increase d. do not change What is the pH of a solution with (HA) = 0.01M and [A] = 0.01M, when pk, = 5.2? (Assume HA and A) are conjugates. a. 5.2 b. 4.2 C. 6.2 d. 7.0 Which solution has a higher ionic strength? A 0.500M solution...
Problem 11.21. For k є Z, we define Ak-{x є Z : x-51+ k for some 1 є z} (a) Prove that {Ak : k Z} partitions Z. (b) We denote by ~ the equivalence relation on Z that is obtained from the par- tition of part (a). Give as simple a description ofas possible; that is, given condition "C(x,y)" on x and y s x~y if and only if "C(x, y)" holds.
Problem 11.21. For k є Z, we...
Let n be a positive integer consisting of up to 8 digits. d8, d7, …..d1.Write a complete C program by usiang a function, to list in one column each of the digits in number n. The right most digit, d1, should be listed at the top of the column. Hint: If If n is 3,407, what is the value of the digit when computed by using digit=n%10; You can test your program for values of n equal to 172,459. So...