1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is

Select one:

a. (−∞,−1]
b. (π,2π)

c. (−∞,−2]
d. (−π,2π)
e. ℝ

f. (−1,∞)

2. The limt→πr(t) where r(t)=〈t2,et,cos(t)〉 is

Select one:

a. 〈π2,eπ,−1〉

b. undefined

c. 〈π2,eπ,1〉
d. π2+eπ
e. 〈π2,eπ,0〉

3.Let v(t)=〈2t,4t,t2〉. Then the length of v′(t) is

Select one:

a. 20‾‾‾√+2t

b. 20+4t2

c. 20+2t‾‾‾‾‾‾‾√

d. 20+4t2‾‾‾‾‾‾‾‾√

e. 6+2t‾‾‾‾‾‾√
f. 1

4. The curvature of a circle centred at the origin with radius 1/3 is

Select one:

a. 1

b. 1/3

c. undefined

d. 3

e. 10

52. Consider the following five statements: i. Swaps may be used to achieve a lower cost of funds for a company. ii. In an interest rate swap, the two parties swap the principal amount plus the ongoing associated interest obligations. iii. An intermediated swap is said to be ‘matched' when a bank enters into swaps with both firms involved in an interest rate swap iv. A ‘plain vanilla' swap is the fixed AUD to floating AUD swap. v. If an intermediary is involved in a swap between two parties, the intermediary will also provide the initial loan to both parties. Which of the following are correct? A. i, ii, iii and iv are true B. ii, iii, iv and v are true C. ii, and iv are true D. i and iii are true

why choose d can help explain why other three are incorrect?????

A Mechanical design company produces an innovative design Component Z100 design of producing one(1) unit of component Z100 is provided in the bill of materials BOM which requires mix shown in Table Q3-1. The current monthly production of Component Z100 is consumption shown in Table Q3-2. Determine the following;

(i) Material usage variance;

(ii) Material price variance;

(iii) Total material cost variance;

(iv) Discuss at least two(2) importance of variance analysis in a manufacturing company

Table Q3-1

Table Q3-2

Choose true or false for each statement regarding the resistance of a wire.
true false  While maintaining a constant voltage V, the current I increases when the length L of a wire increases.
true false  The resistance is proportional to the cross-sectional area A of the wire.
true false  While maintaining a constant voltage V, the current I decreases when the resistivity ρ of a wire decreases.

Choose true or false for each statement regarding resistors in a circuit.
true false  If you connect two different resistors in parallel in a circuit, then the voltage across each of them is different.
true false  If you connect two different resistors in series in a circuit, then the current that flows through each of them is different.
true false  Three identical resistors in parallel have one third the resistance of each individual one.

IP A charge of 21.0 μC is held fixed at the origin. Part A If a -7.00 μC charge with a mass of 3.50 g is released from rest at the position (0.925 m, 1.17 m), what is its speed when it is halfway to the origin? v = m/s Previous AnswersRequest Answer Incorrect; Try Again; 11 attempts remaining Part BPart complete Suppose the -7.00 μC charge is released from rest at the point x = 12(0.925m) and y = 12(1.17m). When it is halfway to the origin, is its speed greater than, less than, or equal to the speed found in part A? Greater than the speed found in part A Lee than the speed found part in A Equal to the speed found in part A Previous Answers Correct Part C Find the speed of the charge for the situation described in part B. v = m/s

1. A 3-phase, 5 kVA, 208 V, 4-pole, 60 Hz, star-connected synchronous generator has negligible stator winding resistance and a synchronous reactance of 8 Ω per phase at the rated terminal voltage. The generator is connected in parallel to a 3-phase, 208 V, 60 Hz infinite bus. All losses may be neglected.

a)   Determine the excitation voltage and the power angle when the machine is delivering rated apparent power at 0.8 PF lagging.

b)   If the field excitation is increased by 20 % without changing the prime mover power, find the stator current, power factor, and reactive power supplied by the machine.

c)   With the field current as in (a), determine the maximum power with which the generator can be supplied without losing synchronism? What are the corresponding stator current and power factor at this maximum power condition?

PLEASE ANSWER ALL 3 WILL THUMBS UP

1) A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 8 m/s. Find the equation of motion.

x(t)=? m

2) Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(γt) V, q(0) = 0 C, and i(0) = 0 A

q(t)= ?

i(t)= ?

3) Find the steady state current i_p(t) in an LRC-series circuit when L = 1/2 h, R= 20 ohms, C= 0.001 f and E(t) = 400sin(60t)+500cos(40t) V

i_p(t)= ?

A 230 V, 500 rpm, 100 A separately- excited dc motor has an armature resistance of 0.1 ohms. The motor is driving, under rated conditions, a load whose torque is constant and independent of speed. The speeds below the rated speed are obtained with armature voltage control (with full field) and the speeds above the rated speed are obtained by field control (with rated armature voltage).

1. What motor terminal voltage is needed to run it at 400 rpm?

2. By what amount should flux be reduced to get a motor speed of 800 rpm?

Neglect the motor’s rotational losses.

3.The separately- excited motor of the previous problem is now coupled to an overhauling load with a torque of 800 N-m. Determine the speed at which the motor can hold the loadby regenerative braking. Source voltage is 230 V. Neglect the motor’s rotational losses.

Three different states participate in a poll of attitudes toward two possible energy policies(Policy I, and Policy II . The results are given in the table below:

State

policy choice Gas Coal Other

I 50 59 161 II 80 71 129

To test the null of association (Independence) between the type of the state and the policy choice. Use ALPHA=.01, then (

A) Test Stat: LaTeX: \chi χ 2 LaTeX: \approx ≈ 10.384 ; p-vLaTeX: \approx ≈ .009 ; Dec: Reject the null

(B) Test Stat: LaTeX: \chi χ 2 LaTeX: \approx ≈ 11.384 ; p-v LaTeX: \approx ≈ .003 ; Dec: Reject the null

(C) Test Stat : LaTeX: \chi χ 2 LaTeX: \approx ≈ 11.384 ; p-v LaTeX: \approx ≈ .030 ; Dec: Reject the null