Prove that ab ≤ 1/2(a2 + b2) for any real numbers a and b.
6. [20] Let A, B e Cnxn such that A2 = A and B2 = B. Prove that if (A + B)2 = A + B, then AB is the zero matrix 0 Rnxn.
Given a second order process: 2 AB → A2 + B2 with k = 0.095 M-1min-1; and the initial concentration of AB = 1.054 M, calculate the concentration of A2 after exactly 30.3 min. Enter the result to 3 decimal places and no units.
The equilibrium constant for the decomposition AB into its elements A2 and B2 has an equilibrium constant of 0.0900 at a given temperature. What is the equilibrium concentration of AB if 0.050 M AB is allowed to decompose? 2 AB(g) ~ A2(g) + B2(g)
2. Consider the reaction A2 + B2 ⇌ 2AB. If the initial concentration of both A2 and B2 is 4.0 M, and after 10 minutes the reaction appears to stop. The concentration of [A2] is now 2.0M. a. Draw a graph of [A2] vs. time, over the span of 20 minutes. b. On the same axes draw a graph of [B2] v time, over a span of 20 minutes. c. On the same axes draw a graph of [AB] v...
2. Consider the reaction A2+ B2 = 2AB. If the initial concentration of both A2 and B2 is 4.0 M. and after 10 minutes the reaction appears to stop. The concentration of [A2) is now 2.0M. a. Draw a graph of [A2) vs. time, over the span of 20 minutes. 09. (M concertuohon 5 15 20 time (min) b. On the same axes draw a graph of [B2] v time, over a span of 20 minutes. c. On the same...
2. Prove that for any fixed real numbers p and g, the equation 2xr + px+q + log2(x2 + px + q) + x2 + px = 2019 has at most two real number solutions. 2. Prove that for any fixed real numbers p and g, the equation 2xr + px+q + log2(x2 + px + q) + x2 + px = 2019 has at most two real number solutions.
Consider the following reaction at 300 K: 2 AB (g) ↔ A2 (g) + B2 (g) In a particular experiment, the partial pressures of A2 and I2 at equilibrium are 0.715 and 0.573 atm, respectively, while the partial pressure of AB is 3.63 atm. What is the equilibrium constant for this reaction?
Consider the following reaction at 300 K: 2 AB (g) ↔ A2 (g) + B2 (g) In a particular experiment, the partial pressures of A2 and I2 at equilibrium are 0.536 and 0.274 atm, respectively, while the partial pressure of AB is 3.382 atm. What is the equilibrium constant for this reaction?
e) Use the triangle inequality to prove that (ac + bd)2 (a2 + b2)(c2 + d2) for all a, b, c, d e R. Total: [20 marks] e) Use the triangle inequality to prove that (ac + bd)2 (a2 + b2)(c2 + d2) for all a, b, c, d e R. Total: [20 marks]
Suppose A and B are matrices with matrix product AB. If bi, b2, ..., br are the columns of B, then Ab, Ab2, ..., Ab, are the columns of AB 1. Suppose A is an nxnmatrix such that A -SDS where D diag(di,d2,... dn) is a diagonal matrix, and S is an invertible matrix. Prove that the columns of S are eigenvectors of A with corresponding eigenvalues being the diagonal entries of D Before proving this, work through the following...