True or False. If true explain or prove answer, and if false give an example to show the statement is not always true.
1. If A is a 4x4 matrix and a1+a2=a3+2a4, then A must be singular.
2. If A is row equivalent to both B and C, then A is row equivalent to B+C.
My Work:
1. I say it's...
Let Ax = b be a linear system whose augmented matrix (A|b) has reduced row echelon form
1 2 0 3 1 ||-2
0 0 1 2 4 || 5
0 0 0 0 0 || 0
0 0 0 0 0 || 0a) Find all solutions to the system
b)If
a1= (1,1,3,4) and a3=...
I still don't understand where -[1/4 +1/2(t-1) -1/4 e^-2(t-1)] U(t-1) comes from. The answer is y= 1/4 + 1/2t +1/4 e^-2t -[1/4 +1/2(t-1) -1/4 e^-2(t-1)] U(t-1). Where does the second part of the answer come from.
I attached the problem as a word document. I'm stuck trying to determine the laplace transform for t-tU(t-1). I know I'm supposed to work with 1/s^2(s+2) and solve for A, B,C. I got B=1/2, A=-1/4, and C=1/4 when 1=(As+B)(s+2)+Cs^2. The answer to the problem is
y= 1/4 + 1/2t +1/4 e^-2t -[1/4...
Find a solution to the following second order differential equation
xy'+y=1/y^2
My Attempt:
P= y'= dy/dx
x dy/dx + y = 1/y^2
dy/dx + y/x = 1/xy^2
Integrating Factor = e^∫1/x dx = e^lnx
y e^lnx=∫ (e^lnx)(1/xy^2) dx
On my test the professor gave us the rate, parameters of A, and temperature of 298K. We were asked to find the activation energy. I know that the Arrhenius equation is LnK= LnA-Ea/RT. However, he did not give us the rate constant "K" instead he gave us the rate. How do you determine activation...
a) Determine K at 298K for the reaction H2(g) + Cl2(g) <---> 2HCl(g)
b) The equilibrium partial pressure of HCl is 1 bar. Determine the equilibrium partial pressures of H2 and Cl2.
This question was on my test. I got K= 3.2 x 10^-34 using dG*=-RTlnK when dG=0 at equilibrium. I'm having...
Hey, I had the same concern. They are both right; it depends on the stoichiometry. The professor would have to specify which one he is looking for like he did last time.
A second- order reaction of the type A + B -->P was carried out in a solution that was initially 0.075 mol dm^-3 in A and 0.050 mol dm^-3 in B. After 1.0 h the concentration of A had fallen to 0.020 mol dm^-3. a) Calculate the Rate constant. b) Solve for the half- life of each of the reactants...