The Law of Biot-Savart shows that the magnetic field of an infinitesimal current element decreases as 1/r^2. Is there anyway you could put together a complete circuit (any closed path of current-carrying wire) whose field exhibits this same 1/r^2 decrease in magnetic field strength? Explain your reasoning.

4. Other things equal, what effect will each of the following changes independently have on the equilibrium level of real GDP in the private closed economy? 1. A decline in the real interest rate. 2. An overall decrease in the expected rate of return on investment. 3. A sizable, sustained increase in stock prices. (answer in your own words)

] Consider the following dynamic equations: ?1̇ = −2?1 + 6?2 ?2̇ = −4?1 + ?(?) ?(?) = ?1 The control is obtained through state feedback with ?(?) = −?1?1 − ?2?2 + ?(?), where ?(?) is reference input. Find the ?1 and ?2 if the closed-loop system has a natural undamped frequency of 10 rad/sec and a damping ratio of 0.707.

The capacitor in the circuit shown in (Figure 1) is charged to an initial value Q. When the switch is closed, it discharges through the resistor. It takes 1.5 seconds for the charge to drop to 12Q.

Part A

How long does it take to drop from initial charge Q to 14Q?

Express your answer to two significant figures and include the appropriate units.

A 65 g ice cube at 0 °C is placed in an insulated box that contains 8 g of steam at 200 °C. What is the equilibrium temperature reached by this closed system? Approximate the specific heat capacity of steam to be 1.5 J/g oC. All the other values can be found on the textbook. [Note: Assume that all of the steam condenses.]

Beginning with all chambers of the heart in the "relaxed" phase, describe the cardiac cycle in mammals, with systole and diastole of the atria and ventricles. For each time point in the cycle you select, state the following:

Whether the atria and ventricles are contracting or relaxing

Whether the AV valves and semilunar valves are closed or open

Whether the pressure in the atria and ventricles is high or low

Please briefly describe the following communication techniques applied to group situations and motivational interviewing/counselling:

a) Active listening

b) Attending skills, use of body language

c) Paraphrasing

d) Reflecting feelings

e) Open and closed questioning or probing

f) Summarizing

g) Reframing

h) Exploring options

I) Normalizing statements

Choose a country of your choice, the key nutrition issues including access to safe drinking water, safety with cooking (such as cooking over an open flame in a closed room) faced by the country, who they most affect, key risk factors, their link with health and economic development, and what might be done to address them in cost-effective ways.

With two examples each, distinguish between the following pairs of terms

a. i. Probability and non-probability sampling                                                        [ 4 Marks ]                             

ii. Open-ended and closed-ended questions                                                      [ 4 Marks ]                              

3. Accessible and target population                                                                  [ 4 Marks ]                            
4. Likert scale and Ranking questions [ 4 Marks ]                                                                                                
5. Multiple choice and contingent questions. [ 4 Marks ]                                                                                       

Robots can be used in manufacturing and assembly operations that require accurate,
fast, and versatile manipulation. The open-loop transfer function of a direct-drive arm may
be approximated by
??(??)??(??) = ??(?? + 10)
??(?? + 3)(??2 + 4s + 8)
a) Determine the value of gain K when the system oscillates,
b) Calculate the roots of the closed-loop system for the K determined in part (a).