1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56.
2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures.
3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by:
T1 exp(^s/Cp) = T2
Where Cp is the specific heat capacity of the gas, ^s is the change of entropy and T1 and T2 are the initial and final temperatures of the process. Determine the value of ^s (units - kJ/kg) if T1 = 320 K, T2 = 450K and Cp = 1.005 kJ/kg K.
4.Transform the formula
Y1 = X1
To make n the subject.
5. Make y the subject of the formula:
E = P(1 - e(y - 1))
6. Given the complex numbers:
z1 = 5 - j4 z2 = 4 + j z3 = -6 - j7 z4 = j2
Calculate, giving answers in the form a +jb, the following:
(i) z4 - z1 + z2
(ii) 3z1 - 2z3 + z4
7. Simplify each of the following giving your answer as a complex number in polar form:
(i) 12 / 40degrees * /135degrees
(ii) 32 /-15 degrees
8 / 48degrees
Logarithm and complex numbers problems are solved.