The relative humidity and specific humidity of the air is 0.01654 and 0.4511 respectively.
What is relative humidity?The amount of moisture in the air is measured relative to the maximum amount of moisture the air can hold at a given temperature. It is given as a percentage.
The relative humidity is 100% when the air contains all of the moisture it can carry at a given temperature. As the temperature drops, so does the quantity of moisture that the air can hold, and the relative humidity rises. In contrast, as the temperature rises, the amount of moisture that the air can hold rises, and the relative humidity falls.
Check the attachment for further details.
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ways of representing spot speed
Answer:
stopwatch method- measures the speed between two points.
radar meter method- uses electromagnetic waves that bounces off of an object causing the wave to change frequency to calculate the speed of the object with a radar machine.
pneumatic road tube method- uses two different tubes to record the time it takes to start and pass through the end line to calculate the speed of the object.
What are the six steps of engineering ( in order)
Answer:
Hope this helps :)
1. Define/Find the problem.
2. Explore/Research/Collect information.
3. Design the best solution base on your ideas/thoughts.
4. Create the solution.
5. Try the creation, put it to test/work.
6. Make the creation better, modify it.
Also, some additional steps are ...
7. Evaluate the solution, finishing thoughts/ideas.
8. Share your results with other engineers/people, final steps
How many FastEthernet interfaces does a 2960 switch have?
Answer:
24 i believe
Explanation:
which of the following is not a performance technique developed by stanislavski? multiple choice through line biomechanics concentration and observation magic if
Through line biomechanics concentration and observation magic if International Society of Biomechanics in sports.
What is "International Society of Biomechanics in sports"?The recently developed professional association in biomechanics is the "International Society of Biomechanics in sports".It is the professional association in bio-mechanics.
It is an international society which is dedicated to bio-mechanics to sports. The main purpose of the society is to understand and study the human movement and its relation to sport bio-mechanics. They provide information regarding bio-mechanics in sports.
Therefore, Through line biomechanics concentration and observation magic if International Society of Biomechanics in sports.
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A wheelbarrow full of concrete mix that needs to be moved onto a platform could be moved either by lifting it above the ground and setting it onto the platform or by using an inclined plane. The advantage of using the inclined plane is that the work can be done -
The force over the inclined plane required to elevate the barrow is less than the straight surface as there was the tangential gravitational force acting on the barrow.
What is force?The force is the push or pulls experienced by the object when interacting with the other object. The force applied is calculated with respect to the force experienced by the object.
On moving the wheelbarrow over a straight surface, the gravitational force acting over it requires more force to elevate it in the opposite spatial relation.
Over the inclined plane, the wheelbarrow experiences the tangent of the gravitational force over it, and less force is required to elevate the barrow to the same level as the straight surface.
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how many dfma principals are used in concurrent engineering
Answer:
aqswdefrtghyujkijuhygtfrdesw
Explanation:
when analyzing data sets, such as data for human heights or for human weights, a common step is to adjust the data. this adjustment can be done by normalizing to values between 0 and 1, or throwing away outliers. for this program, adjust the values by dividing all values by the largest value. the input begins with an integer indicating the number of floating-point values that follow. output each floating-point value with two digits after the decimal point, which can be achieved as follows: print(f'{your value:.2f}')
The java program to illustrate the data set will be;
import java.util.Scanner;
public class LabProgram {
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int n;
n = scan.nextInt();
while(n<=0){
n = scan.nextInt();
}
float val[] = new float[n];
for(int i = 0;i<val.length;i++){
val[i] = scan.nextFloat();
}
float max = val[0];
for(int i = 1;i<val.length;i++){
if(max < val[i]){
max = val[i];
}
}
for(int i = 0;i<val.length;i++){
val[i] = val[i]/max;
}
for(int i = 0;i<val.length;i++){
System.out.printf("%.2f ",val[i]);
}
System.out.println();
}
}
What is a java program?Java is a high-level, broad, object-oriented, and secure programming language created by Sun Microsystems, Inc.'s James Gosling in 1991.
Java programs are frequently asked about during interviews. These programs can be accessed via control statements, arrays, strings, oops, and so on.
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Which XXX outputs the following? You have 3 Pencils. Total Price: 60 #include #include typedef struct Data_struct { int itemCount; double price; char name[20]; } Data; Data myData; void updateltemCount(int x) { myData.itemCount = x; } void updateltemPrice(double p) { myData.price = p; } void updateltemName(char n[20]) { strcpy(myData.name,n); }
double totalPrice() { XXX } int main(void) { int number = 3; double price = 20.0; char name[] = "Pencil"; double total; updateltemCount(number); updateltemPrice(price); updateltemName(name); total = totalPrice(); printf("You have %d %ss.", number, name); printf("Total Price: %.Of", total); return 0; } O return itemCount * price; return myData.itemCount * myData.price; 0 return price * number; total = myData.itemCount * myData.price;
The XXX output of the following coding is return myData.itemCount * myData.price;. The correct option is B.
What is the output?The output, which might take the form of text on a screen, printed materials, or sound coming from a speaker, is how the computer displays the outcomes of the operation.
totalPrice() function returns a double value.
So, XXX should be a return statement.
We can access itemCount of myData using
myData.itemCount
We can access pri
ce of myData using
myData.price
So, the return statement should be
return myData.itemCount * myData.price;
Therefore, the correct option is B. return myData.itemCount * myData.price;.
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a weight of 20 lb is applied to a cylinder that is full of water. The Piston area is 4.5 inches squared. what is the pressure of the water? round to one "decimal" place.
Answer:
6.564 is the answers i learned that in the american school i live there
In the circuit of Figure 1, V = 277 volts, L = 2 mH, R = 0:4 Ω, and Ï = 2Ï60 rad/s. Determine (a) the rms symmetrical fault current; (b) the rms asymmetrical fault current at the instant the switch closes, assuming maximum dc offset; (c) the rms asymmetrical fault current 5 cycles after the switch closes, assuming maximum dc off-set; (d) the dc offset as a function of time if the switch closes when the instantaneous source voltage is 300 volts.
(a) The rms symmetrical fault current is 326.65 A
(b) The rms asymmetrical fault current at the instant the switch closes, assuming maximum dc offset is 397.4π A
(c) The rms asymmetrical fault current 5 cycles after the switch closes, assuming maximum dc off-set is 324.539 A
(d) The dc offset as a function of time if the switch closes when the instantaneous source voltage is 300 volts is 351.43\(e^{200t}\) A
What is symmetrical fault current?Transmission line faults can generally be divided into the following categories:
Symmetrical faultsAsymmetrical faultsA symmetrical fault in a power system is a type of fault that results in a short circuit involving all three phases. This could be a three phase short circuit or a three phase to ground fault.
When a fault is symmetrical, fault currents in the phases are symmetrical in that their magnitudes are equal and they are equally spaced by a 120° angle. So, a symmetrical fault with a high value of current in phases may be taken for granted as the norm.
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Determine (a) the peak frequency deviation, (b) minimum bandwidth,and (c) baud for a binary FSK signal with a mark frequency of 38 kHz, a space frequency of 40 kHz, and an input bit rate of 4 kbps
The peak frequency deviation, minimum bandwidth, and baud for a binary FSK signal for the given frequencies are respectively;
a) 0.5 kHz
b) 9 kHz
c) 4000
Peak frequency deviation1) The peak frequency deviation is gotten from the formula;
∆f = |f_m - f_s|/f_b
where;
f_m is mark frequencyf_s is space frequencyf_b is input bit rateThus;
∆f = |38 - 40|/4
∆f = 0.5 kHz
2) The minimum bandwidth is given by the formula;
B = 2(∆f + f_b)
B = 2(0.5 + 4)
B = 9 kHz
3) For FSK signal, N = 1, and the baud is gotten from the Equation;
baud = f_b/1
f_b = 4 kbps = 4000 bps
Thus; baud = 4000/1 = 4000
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PLEASE FILL IN BLANK WITH CORRECT ANSWER
1. We cannot solve _____ by simplex.
2. In any integer basic feasible solution of the _____, the number of positive variables is equal to half the number of functional constraints.
3. A discrete dynamic programming problem can be represented by a _____.
4. A tree is a special case of a _______.
1. We cannot solve nonlinear programming problems by simplex.The simplex method is utilized for linear programming problems only. The LP problems have linear constraints and a linear objective function. The nonlinear programming problems cannot be solved by the simplex method.
We have to use the other methods for these kinds of issues.2. In any integer basic feasible solution of the transportation problem, the number of positive variables is equal to half the number of functional constraints. It is feasible to use a solution that is restricted to whole numbers for transportation problems. We've got a few formulas that can help us figure out the answers.3. A discrete dynamic programming problem can be represented by a tree. To solve a dynamic programming problem, we typically use a graph structure known as a decision tree. The nodes of a decision tree represent decision points, and the arcs represent the choices available at each decision point.4. A tree is a special case of a graph. Trees are a special kind of graph, so it makes sense that they're also used to represent decision trees. Trees are graphs with nodes linked together in a particular manner. There is a parent-child relationship between the nodes of a tree, which means that each node has only one parent and zero or more children. Trees have no cycles, which means that there is no way to traverse the tree from a node to itself without first traversing a node that is not a descendant.
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A piston-cylinder device contains nitrogen gas. During a reversible, adiabatic process, the entropy of the nitrogen will always increase: Select one: a. Always b. Sometimes c. None of the mentioned d. Never
During a reversible, adiabatic process, the entropy of the nitrogen will never always increase. Option D
What is a reversible adiabatic process?In a reversible, adiabatic process, the entropy of an ideal gas remains constant.
This is known as the isentropic process.
The increase in entropy is related to the irreversible nature of a process and the transfer of heat from a high-temperature reservoir to a low-temperature reservoir.
However, in an adiabatic process, there is no transfer of heat and the process is reversible, meaning that the entropy of the nitrogen will remain constant.
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why you so mean to me? leave my questions please. answer them
Answer: Why is even here then.
Explanation:
Complete the following sentence.
Geometry is a field of ____ that studies the size, shape, and position of structures by analyzing space.
Answer:
Mathematics
Explanation:
⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄
Answer:
It is a field if mathematics
1.3. If the surface tension coefficient of a fluid is 0,07 N/m and the radius
of the droplet is 2,5 mm. calculate:
1.3.1 surface tension force
(2)
1.3.2 difference in pressure of the droplet
(1)
Answer:
A) F = 0.011 N
B) ΔP = 5.6 N/m²
Explanation:
We are given;
surface tension coefficient; S = 0.07 N/m
Radius; r = 2.5 mm = 0.025 m
A) Formula to find the surface tension force(F) is given by;
F = SL
Where L is effective length = 2πr
F = 0.07 × 2π × 0.025
F = 0.011 N
B) Formula for difference in pressure droplet is;
ΔP = 2S/r
Thus;
ΔP = (2 × 0.07)/0.025
ΔP = 5.6 N/m²
An o ring intended for use in a hydraulic system using MIL-H-5606 (mineral base) fluid will be marked with
An o ring intended for use in a hydraulic system using MIL-H-5606 (mineral base) fluid will be marked with a blue stripe or dot.
Considering the CIA triad and the Parkerian hexad, what are the advantages and disadvantages of each model?
The CIA triad and the Parkerian hex are the fundamental principles of information security.
CIA triad and the Parkerian hexadParkeriano, or Parkerian hexad: is a set of six elements of information security proposed by Donn B. Parker.
1. Confidentiality.
2. Ownership or Control.
3. Integrity.
4. Authenticity.
5. Availability.
6. Utility
The Parkerian hexagram adds three more attributes to the three classic security attributes of the CIA triangle
Confidentiality Integrity Availability
these are the fundamental principles of information security.
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Where would an engineer indicate the unit of measurement used in a design
An engineer would indicate the unit of measurement used in a design in millimeters.
What are measurements?The primary unit of measurement is the stocking unit of measure for a given item in a specific organization. You must define an item attribute that serves as the primary unit of measurement when creating each item.
Because the technical drawings are scaled, engineers, architects, and builders may create the items according to exact specifications.
When understanding scales, the number on the left relates to the measurement of the drawing, while the number on the right represents the actual size of the object.
Therefore, a millimeter is used in a design.
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Any one know the answer?
Answer:
151.2 N
Explanation:
The upward force at A is 135/(135+325) times the total weight of the generator. The CW torque about point O that produces is ...
(460 mm)(135/460)(160 kg)(9.8 m/s^2) = 211.68 N·m
For F to produce half that torque, it must be ...
F(0.7 m) = (211.68 N·m)/2
F = 211.68 N·m/(1.4 m) = 151.2 N
The wheel and the attached reel have a combined weight of 50lb and a radius of gyration about their center of 6 A k in = . If pulley B that is attached to the motor is subjected to a torque of M ft lb = − 50 , determine the velocity of the 200lb crate after the pulley has turned 5 revolutions. Neglect the mass of the pulley
The complete question is;
The wheel and the attached reel have a combined weight of 50 lb and a radius of gyration about their center of ka = 6 in. If pulley B that is attached to the motor is subjected to a torque of M = 50 lb.ft, determine the velocity of the 200lb crate after the pulley has turned 5 revolutions. Neglect the mass of the pulley.
The image of this system is attached.
Answer:
Velocity = 11.8 ft/s
Explanation:
Since the wheel at A rotates about a fixed axis, then;
v_c = ω•r_c
r_c is 4.5 in. Let's convert it to ft.
So, r_c = 4.5/12 ft = 0.375 ft
Thus;
v_c = 0.375ω
Now the mass moment of inertia about of wheel A about it's mass centre is given as;
I_a = m•(k_a)²
The mass in in lb, so let's convert to slug. So, m = 50/32.2 slug = 1.5528 slug
Also, let's convert ka from inches to ft.
So, ka = 6/12 = 0.5
So,I_a = 1.5528 × 0.5²
I_a = 0.388 slug.ft²
The kinetic energy of the system would be;
T = Ta + Tc
Where; Ta = ½•I_a•ω²
And Tc = ½•m_c•(v_c)²
So, T = ½•I_a•ω² + ½•m_c•(v_c)²
Now, m_c is given as 200 lb.
Converting to slug, we have;
m_c = (200/32.2) slugs
Plugging in the relevant values, we have;
T = (½•0.388•ω²) + (½•(200/32.2)•(0.375ω)²)
This now gives;
T = 0.6307 ω²
The system is initially at rest at T1 = 0.
Resolving forces at A, we have; Ax, Ay and Wa. These 3 forces do no work.
Whereas at B, M does positive work and at C, W_c does negative work.
When pulley B rotates, it has an angle of; θ_b = 5 revs × 2π rad/revs = 10π
While the wheel rotates through an angle of;θ_a = (rb/ra) • θ_b
Where, rb = 3 in = 3/12 ft = 0.25 ft
ra = 7.5 in = 7.5/12 ft = 0.625 ft
So, θ_a = (0.25/0.625) × 10π
θ_a = 4π
Thus, we can say that the crate will have am upward displacement through a distance;
s_c = r_c × θ_a = 0.375 × 4π
s_c = 1.5π ft
So, the work done by M is;
U_m = M × θ_b
U_m = 50lb × 10π
U_m = 500π
Also,the work done by W_c is;
U_Wc = -W_c × s_c = -200lb × 1.5π
U_Wc = -300π
From principle of work and energy;
T1 + (U_m + U_Wc) = T
Since T1 is zero as stated earlier,
Thus ;
0 + 500π - 300π = 0.6307 ω²
0.6307ω² = 200π
ω² = 200π/0.6307
ω² = 996.224
ω = √996.224
ω = 31.56 rad/s
We earlier derived that;v_c = 0.375ω
Thus; v_c = 0.375 × 31.56
v_c = 11.8 ft/s
Draw an ERD for each of the following situations. (If you believe that you need to make additional assumptions, clearly state them for each situation.) Draw the same situation using the tool you have been told to use in the course. a. A company has a number of employees. The attributes of EMPLOYEE include Employee ID (identifier), Name, Address, and Birthdate. The company also has several projects. Attributes of PROJECT include Project ID (identifier), Project Name, and Start Date. Each employee may be assigned to one or more projects or may not be assigned to a project. A project must have at least one employee assigned and may have any number of employees assigned. An employee's billing rate may vary by project, and the company wishes to record the applicable billing rate (Billing Rate) for each employee when assigned to a particular project. Do the attribute names in this description follow the guidelines for naming attributes? If not, suggest better names. Do you have any associative entities on your ERD? If so, what are the identifiers for those associative entities? Does your ERD allow a project to be created before it has any employees assigned to it? Explain. How would you change your ERD if the Billing Rate could change in the middle of a project? b. A laboratory has several chemists who work on one or more projects. Chemists also may use certain kinds of equipment on each project. Attributes of CHEMIST include Employee ID (identifier), Name, and Phone No. Attributes of PROJECT include Project ID (identifier) and Start Date. Attributes of EQUIPMENT include Serial No and Cost The organization wishes to record Assign Date—that is, the date when a given equipment item was assigned to a particular chemist working on a specified project A chemist must be assigned to at least one project and one equipment item. A given equipment item need not be assigned, and a given project need not be assigned either a chemist or an equipment item. Provide good definitions for all of the relationships in this situation. c. A college course may have one or more scheduled sections or may not have a scheduled section. Attributes of COURSE include Course ID, Course Name, and Units. Attributes of SECTION include Section Number and Semester ID. Semester ID is composed of two parts: Semester and Year. Section Number is an integer (such as 1 or 2) that distinguishes one section from another for the same course but does not uniquely identify a section. How did you model SECTION? Why did you choose this way versus alternative ways to model SECTION? d. A hospital has a large number of registered physicians. Attributes of PHYSICIAN include Physician ID (the identifier) and Specialty. Patients are admitted to the hospital by physicians. Attributes of PATIENT include Patient ID (the identifier) and Patient Name. Any patient who is admitted must have exactly one admitting physician. A physician may optionally admit any number of patients. Once admitted, a given patient must be treated by at least one physician. A particular physician may treat any number of patients, or may not treat any patient& Whenever a patient is treated by a physician, the hospital wishes to record the details of the treatment (Treatment Detail). Components of Treatment Detail include Date, Time, and Results. Did you draw more than one relationship between physician and patient? Why or why not? Did you include hncnithi ac an antitv type? Why or why not?
Answer:
it wqas red
Explanation:
red
what is the voltage in the secondary winding of the transformer if the primary voltage is 120v and the turns ratio is 6:1
Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s. The turbine operates at steady state and develops a power output of 2500 kW. Heat transfer between the turbine and its surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air and the exit area.
This question is incomplete, the missing diagram is uploaded along this answer below.
Answer:
- The mass flow rate of air is 4.59 kg/s
- Area of the exit turbine is 0.066 m²
Explanation:
Given the data in the question;
Using air as an ideal gas.
Turbine;
state 1: p₁ = 8 bar, T₁ = 960 K
state 2: p₂ = 1 bar, T₂ = 450 K
The inlet velocity is small compared to the exit velocity of 90 m/s
V₁ < V₂ = 90 m/s
Power of turbine W' = 2500 kW
Now, lets assume Q = 0 and ΔPE = 0
we know that; R = 0.2870 kJ/kg-K
Also. \(C_p\) at 700K = 1.075 kJ/kg-K
Now, using ideal gas law;
STATE1
v₁ = RT₁/p₁
so we substitute
v₁ = [(0.2870 kJ/kg-K)(960 K)/(8 bars )]|\(\frac{bar}{10^5N/m^2}\)||\(\frac{1000N.m}{kJ}\)| = 0.344 m³/kg
STATE2
v₂ = RT₂/p₁
we substitute
v₂ = [(0.2870 kJ/kg-K)(450 K)/(1 bars )]|\(\frac{bar}{10^5N/m^2}\)||\(\frac{1000N.m}{kJ}\)| = 1.2915 m³/kg
Now, from energy balance steady state;
0 = Q" - W" + \(m"_i\)( \(h_i\) + \(\frac{V_i^2}{2}\) + \(gz_i\)) - \(m"_B\)( \(h_B\) + \(\frac{V_B^2}{2}\) + \(gz_B\))
since we initially assume Q = 0 and ΔPE = 0
hence;
0 = \(-\frac{W"}{m"}\) + h₁ + \(\frac{V_1^2}{2}\) - h₂ + \(\frac{V_2^2}{2}\)
\(\frac{W"}{m"}\) = h₁ + \(\frac{V_1^2}{2}\) - h₂ + \(\frac{V_2^2}{2}\)
⇒ \(\frac{W"}{m"}\) = \(C_p\)(T₁ - T₂) + \(\frac{1}{2}\)( V₁² - V₂²)
we solve for m"
m" = W" / (\(C_p\)(T₁ - T₂) + \(\frac{1}{2}\)( V₁² - V₂²))
so we substitute;
m" = {[2500 kW] / [(1.075kJ/kg-K(960K - 450k) + \(\frac{1}{2}\)( (0)² - (90 m/s)²)) |kJ/1000N.m| |N/kg.m/s²|]} | kJ/s / kW|
m" = 4.59 kg/s
Therefore, the mass flow rate of air is 4.59 kg/s
From the mass body steady state;
0 = m"₁ - m"₂
so
m"₁ = m"₂ = 4.59 kg/s
now, the volumetric flow rate V"₂ will be;
V"₂ = m" × v₂
we substitute
V"₂ = 4.59 kg/s × 1.2915 m³/kg = 5.93 m³/s
and
the volumetric flow rate V"₂ = A₂V₂
so;
Exit Area A = V"₂ / V₂
we substitute
A = (5.93 m³/s ) / (90 m/s)
A = 0.06589 ≈ 0.066 m²
Therefore, Area of the exit turbine is 0.066 m²
19) The stator winding of a three-phase motor is often referred to as
a. motor primary
b. motor secondary
c. phase primary
d. phase secondary ransfor
The stator winding of a three-phase motor is often referred to as the motor primary. So, the correct choice is option a.
In a three-phase motor, the stator winding is responsible for creating the rotating magnetic field necessary for the motor's operation. It is called the "primary" because it is the primary source of electromagnetic power in the motor. The stator winding consists of coils of wire that are carefully arranged and connected to form three phases: A, B, and C. When an alternating current is passed through the stator winding, it generates a rotating magnetic field. This magnetic field interacts with the rotor, which is the rotating part of the motor, causing it to rotate and produce mechanical power.
The term "primary" is used to distinguish the stator winding from the "secondary" winding, which is found in certain types of motors like transformers. In transformers, the primary winding receives electrical power and transfers it to the secondary winding through electromagnetic induction. However, in a three-phase motor, the stator winding is the primary source of power that initiates the rotation and provides the driving force. It is crucial for generating the magnetic field that interacts with the rotor to convert electrical energy into mechanical energy.
Therefore, referring to the stator winding of a three-phase motor as the motor primary accurately describes its role and its significance in the motor's operation.
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QUESTION ONE Write short answers on the following questions: i. Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below: Rain Gauge Number 1 2 3 4 5 6 Rainfall Depth (mm) 470 465 435 525 480 510 Area of Thiessen Polygon (x104 m²) 95 100 98 80 85 92 The Thiessen mean value (in mm, up to one decimal place) of the rainfall is
Answer:
identify function of the system unit and its components
In order for communication to be considered two-way, _________ is necessary a. channel b. message c. noise d. feedback e. circuit
Answer:
the answer c or e or do wha t the first guy do
A _________ conversion involves running the old and new systems simultaneously for a time, which is is rarely used, since it impractical for customer-facing e-commerce systems.
Compare and contrast direct conversion and parallel conversion.
what is the exact process involved?
Both conversion tactics center on how users are transitioned to the new system. The old system is "unplugged" and the new system is turned on in a direct conversion. The new system must be used by the users; they have no other option. The old system is temporarily used while the new system is activated in the parallel conversion plan. The direct approach is obviously more dangerous because there is no backup in the event that severe system problems are found.
If a significant flaw in the new system is found, the parallel conversion will keep the old system operational. However, the expense and additional work of utilizing both systems at once must be taken into account.
Hence to conclude Compare and contrast direct conversion and parallel conversion involves running the old and new systems
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The primary energy source that operates a building's air conditioning controller is typically electric, pneumatic, or
A. thermostatic.
B. passive.
C. electronic.
D. hydraulic.
Answer:
(c) electronic
Explanation:
for pf, this is correct....Here is the sentence from the pf lesson
" The primary energy source for the controller within buildings is typically electric, pneumatic, or
electronic
."
2. We consider the equations of motion of a linearized inverted pendulum \[ J_{t} \ddot{x}+\gamma \dot{x}-m g \ell x=u . \] Here, \( x \) denotes the angle of the pendulum where \( x=0 \) corresponds
The equation of motion of a linearized inverted pendulum is given by;
\($$J_t \ddot{x} + \gamma \dot{x} - mglx = u$$\)
Here, \(x\) represents the angle of the pendulum such that \(x=0\) represents the equilibrium position of the pendulum when it is pointing downwards. The other parameters are as follows;\(J_t\) - the moment of inertia of the pendulum\(\gamma\) - coefficient of friction between the pendulum and air resistance\(m\) - the mass of the pendulum\(\ell\) - the length of the pendulum\(g\) - the acceleration due to gravity\(u\) - the control inputThe equation of motion shows the relationship between the angle of the pendulum, its angular acceleration, and the control input.
The equation shows that the angular acceleration of the pendulum is proportional to the control input and inversely proportional to the moment of inertia. It is also proportional to the length of the pendulum and the sine of the angle of inclination. The equation of motion also shows that the angular acceleration of the pendulum is damped due to the friction and air resistance. This makes the pendulum come to rest after some time even without external control.The above equation can be solved using Laplace transforms. Let
\(\(x(s) = \mathcal{L} \{x(t)\}\)\(u(s)\)= \(\mathcal{L} \{u(t)\}\)\)
Then we have
\($$J_ts^2x(s) + \gamma s x(s) - mglx(s) = u(s)$$$$x(s) = \frac{1}{J_ts^2 + \gamma s - mgl} u(s)$$Therefore$$x(t) = \mathcal{L}^{-1} \{\frac{1}{J_ts^2 + \gamma s - mgl} u(s)\}$$\)
The Laplace transform can be used to find the response of the pendulum to different inputs, such as a step input or a sinusoidal input.
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