Problem 13.2: Where on the parametrized surface ~r(u; v) = [1 +
u³,v²,uv]^T is the temperature T(x, y, z) = 2 + x + 12y - 12z minimal?
To nd the minimum, look where the function f(u; v) = T(~r(u, v)) has an
extremum. Find all local maxima, local minima or saddle points of f.

Suppose that a parallel-plate capacitor has circular plates with radius R = 18 mm and a plate separation of 3.6 mm. suppose also that a sinusoidal potential difference with a maximum value of 153 V and a frequency of 60 Hz is applied across the plates: that is, V = (153 V) sin[2 ?(60 Hz)t] Find Bmax, the maximum value of the induced magnetic that occurs at r = R.

In which of the following cases did the court decide that in trying to ascertain whether a statement is a term or not the relative knowledge of the parties is a relevant consideration?

a). Hopkins v Tanqueray (1854) 15CB 130.

b). Pym v Campbell (1856) 6 & B 370.

c). Oscar Chess v Williams [1957] 1 ALL ER 325.

d). All of the answers provided.

Thanks for answering!

7. Given the standard reduction potential for the following two half-cell reactions (in the presence of 1.00 M HCl):

Fe3+ + e <==> Fe2+, E0 = + 0.68 V

AsO4 - + 2H+ + 2e <==> AsO3 - + H2O, Eo = +0.559 V.

Please calculate the system potential at the equivalence point when Fe3+ was used to titrate AsO3 - in the presence of 1.00 M HCl.

Answer: 0.60 V

[BI A 30kVA, 3000/1 1 0 V transfomier, the following experimental data was obtained:
0.C test: 3000 V, 0.5 A,
350 W
S.C test: 150 V, 10 A,
500 W
Calculate (a) the efficiency at full load, 0.8p.f. (b) the kVA output at which the efficiency
is ma)cimum (comment on the obtained resu]ts)f 1 5 Marks]

Q2.Find the equivalent circuit from no - load and short - circuit test of a 3 - phase. 14.92 kW, 400 V, 6 - pole induction motor from the following test results (line values): No - load: 400 - V, 11 A, p.f. = 0.2 Short - circuit: 100 - V, 25 A, p.f. = 0.4 Rotor Cu loss at standstill is half the total Cu loss.

A 32.0-μF capacitor is connected to a 53.0-Ω resistor and a generator whose rms output is 30.0 V at 60.0 Hz.

(a) Find the rms current in the circuit.
______ A

(b) Find the rms voltage drop across the resistor.
______ V

(c) Find the rms voltage drop across the capacitor.
_______ V

(d) Find the phase angle for the circuit.
The voltage _______ leads ahead of lags behind the current by _____°.

PART 1

In the laboratory, a general chemistry student measured the pH of a 0.321 M aqueous solution of caffeine, C₈H₁₀N₄O₂ to be 12.045.

Use the information she obtained to determine the K_b for this base.

K_b(experiment) = _____

PART 2

In the laboratory, a general chemistry student measured the pH of a 0.551 M aqueous solution of trimethylamine, (CH₃)₃N to be 11.754.

Use the information she obtained to determine the K_b for this base.

K_b(experiment) = _____

PART 3

In the laboratory, a general chemistry student measured the pH of a 0.562 M aqueous solution of codeine, C₁₈H₂₁O₃N to be 10.834.

Use the information she obtained to determine the K_b for this base.

K_b(experiment) = _____

A random variable Y whose distribution is binomial with parameters are n = 500 and p= 0.400, and here Y suggests the number of desired outcomes of the random experiment and n-Y is the number of undesired outcomes obtained from a random experiment of n independent trials. On this random experiment   p̂ sample proportion is found as Y/n. (Round your answers to 3 decimal places in all parts.)

a)What is the expected value of this statistic?

b)Between what limits will 99% of the sample proportion occur?

c)What is the probability that sample proportion exceed 0.456?

d). What is the probability that sample proportion less than 0.344?