Answer:
1) the volume of solid (Vs) is 4733.33 ft³
2) the total cost to pay Pit A is $58220
3) the total cost to pay to Pit B is $53344.67
4) the total cost to pay to Pit C is $34269.32
5) the total cost to pay to Pit D is $49132.02
Explanation:
given the data in the question;
Vs = ?, V = 7100 ft³, e = 0.5
1) Calculate the volume of solid (Vs)
Vs = V / ( 1 + e )
we substitute
Vs = 7100 / ( 1 + 0.5 )
Vs = 7100 / 1.5
Vs = 4733.33 ft³
Therefore, the volume of solid (Vs) is 4733.33 ft³
2) Calculate the total cost to pay to Pit A
VpitA / Vcomp = ( 1 + e\(_{PHA}\)) / ( 1 + e\(_{comp\) )
we substitute
VpitA / 7100 = ( 1 + 1.5) / ( 1 + 0.5)
VpitA / 7100 = 1.3666666
VpitA = 1.3666666 × 7100
VpitA = 9703.33 ft³
Total cost = volume × unit cost = 9703.33 ft³ × 6 = $58220
Therefore, the total cost to pay Pit A is $58220
3) Calculate the total cost to pay to Pit B = Borrow Pit C: void ratio = 0.81 and the unit cost = $ 4 /ft3
Vpitb / Vcomp = ( 1 + e\(_{PHB}\)) / ( 1 + e\(_{comp\) )
we substitute
VpitB / 7100 = ( 1 + 0.61) / ( 1 + 0.5)
VpitB / 7100 = 1.0733333
VpitB = 1.0733333 × 7100
VpitB = 7620.666 ft³
Total cost = volume × unit cost = 7620.666 × 7 = $53344.67
Therefore, the total cost to pay to Pit B is $53344.67
4) Calculate the total cost to pay to Pit C = Borrow Pit D: void ratio = 0.73 and the unit cost = $6 /ft3
VpitC / Vcomp = ( 1 + e\(_{PHC}\)) / ( 1 + e\(_{comp\) )
we substitute
VpitC / 7100 = ( 1 + 0.81) / ( 1 + 0.5)
VpitC / 7100 = 1.2066666
VpitC = 1.2066666× 7100
VpitC = 8567.33 ft³
Total cost = volume × unit cost = 8567.33 × 4 = $34269.32
Therefore, the total cost to pay to Pit C is $34269.32
5) Calculate the total cost to pay to Pit D
VpitD / Vcomp = ( 1 + e\(_{PHD}\)) / ( 1 + e\(_{comp\) )
we substitute
VpitD / 7100 = ( 1 + 0.73) / ( 1 + 0.5)
VpitD / 7100 = 1.1533333
VpitD = 1.1533333 × 7100
VpitD = 8188.67 ft³
Total cost = volume × unit cost = 8188.67 × 6 = $49132.02
Therefore, the total cost to pay to Pit D is $49132.02
Determine the value of floor(lg(n)) for n = 63.
The value of floor(lg(n)) for n = 63 is found to be 5.
To determine the value of floor(lg(n)) for n = 63, we can calculate the base-2 logarithm of 63 and round down to the nearest integer.
The base-2 logarithm, denoted as lg(n), represents the exponent to which 2 must be raised to obtain the value of n. In this case, lg(63) is approximately 5.977, but since we need to round down, the result is 5.
Therefore, the value of floor(lg(n)) for n = 63 is 5.
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The primary characteristic of oil that affects a service technician is its_________________.
Volatility
Lubricity
Brand
Viscosity
Answer:
ABCD
Explanation:
Couette flow is zero fluid slip at the boundary or boundaries, such as a sliding rigid plate, (ski or sled on a melted snow film), or a cylinder sliding along a tube (an oiled piston or projectile in a air-filled gun barrel), or a shaft rotating in a supporting bearing.
a. True
b. False
Couette flow is a type of fluid flow in which a viscous fluid is confined in a space between two surfaces, which move with respect to each other, producing a shearing motion within the fluid.
In this type of flow, the velocity profile is linear with zero velocity at the surface, which means there is zero fluid slip at the boundary or boundaries such as a sliding rigid plate, a cylinder sliding along a tube, or a shaft rotating in a supporting bearing.
Hence, the given statement is true, which means option (a) is correct.However, Couette flow is the flow of a fluid in a thin layer between two parallel surfaces, where the flow is driven by the motion of one of the surfaces relative to the other. As a result of this motion, there is a velocity gradient within the fluid, which is proportional to the distance from the stationary surface. Couette flow can be used to model fluid flow in many practical engineering applications, such as lubrication in bearings, flow through pipes, and the operation of turbines and pumps.
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Technician A says independent shops are not affiliated with vehicle manufacturers, but it is easy for technicians who work in these shops to get manufacturer training on new technologies. Technician B says independent shops are not affiliated with vehicle manufacturers, making it harder for independent technicians to access training on new vehicle technology. Who is correct? Technician A Technician A Both A and B Both A and B Neither A nor B Neither A nor B Technician B Technician B
Answer:
b
Explanation:
i did it yeater dayajsbs
Refrigerant 134a passes through a throttle valve as part of a refrigeration cycle. The fluid enters the valve as compressed liquid at a pressure of 0.8 MPa and a temperature of 25 C. It exits the valve at -20 C. Find the exit pressure and the exit specific internal energy.
The exit pressure will be 1.3273 bar = 0.1327 MPa and the exit specific internal energy 228.61 KJ/Kg .
1.) In graph,
1-2 = Compressor
3-4 = Throttle value
\(T_{1} \\\) = \(T_{4}\) = -20°C = 253 K
\(T_{3}\) = 25°C = 298 K
\(P_{3}\) = 0.8 MPa
Assuming saturated fluid is entering the value at point (3),
using table of R-134a properties
∵ \(h_{3} =h_{4}\) = 234.49 KJ/Kg (at 25°C,8 bar)
at \(T_{3}\) = 25° , \(P_{3}\) = 0.8 MPa =8 bar
At -20°C, \(hf_{4}\) = 173.6 KJ/Kg
\(hg_{4}\) = 386.6 KJ/Kg
\(h_{4} = hf_{3} + n_{4} ( hg_{4} - hf_{4} )\) = 234.49
173.6 + \(n_{4}\) [386.6 - 173.6] = 234.49
\(n_{4}\) = 0.285
\(P_{4} = P_{1} = P_{sat}\) = 1.3273 bar = 0.1327 MPa
2.)
Exit specific internal energy, using table R-134a
\(U_{4} = uf_{4} + n_{4} (ug_{4} - uf_{4} )\)
at -20°c, \(uf_{4}\\\) = 173.65, ufg = 192.85 KJ/ Kg
\(U_{4}\) = 173.65 + 0.285 (192.85)
\(U_{4}\) = 228.61 KJ/Kg
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Social networking can leave you exposed to criminal activity in the following ways EXCEPT _____.
A. Tracking your online activity and then selling that data without your knowledge
B. Using your photos and posts to form impressions about your character
C. Alerting others that you are not home according to location-tracking features
D. Enticing you to friend someone so that they gain access to your account
A. Tracking your online activity and then selling that data without your knowledge.
Social networking can make users vulnerable to various criminal activities, including identity theft, cyberbullying, and scams. One of the most significant risks is the exposure of personal information, which can be used for targeted advertising, phishing, or even physical harm. Cybercriminals can use social media to track users' online activity and collect personal data without their knowledge or consent, which can be sold or used for identity theft. Moreover, criminals can use social media to spread malicious content or gain access to user accounts, posing as trustworthy friends or authority figures. Therefore, users should be aware of the risks and take measures to protect their privacy and security, such as reviewing privacy settings, avoiding sharing sensitive information, and being cautious about accepting friend requests from unknown users.
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Dirty lens of headlights can reduce light by up to ____.
a)15%
b)40%
c)60%
d)90%
c
it could not be d it cover about all the lights u would have to have thick dirt can't be a way to little dirt u would have to just throw dirt on ur lights and b same thing to little amount of dirt
What are the major types of interior walls and partitions in a larger building, such as a hospital, classroom building, apartment building, or office building? How do these types differ from one another? Why is gypsum used so much in interior finishes? Name the coats of plaster used over expanded metal lath and explain the role of each. Under what circumstances would you specify the use of portland cement plaster? Keenes cement plaster? Veneer plaster? Describe step by step how the joints between sheets of gypsum board are made invisible. List the potential range of functions of a finish ceiling and of a finish floor. What are the advantages and disadvantages of a suspended ceiling compared to those of a tightly attached ceiling? When designing a building with its structure and mechanical equipment left exposed at the ceiling, what precautions should you take to ensure a satisfactory appearance? What does underlayment do? How should it be laid? List several different approaches to the problem of running electrical and communications wiring beneath a floor of a building framed with steel or concrete
The major types of interior walls and partitions in a larger building are:
Fire wallFire barrierSmoke barrierWhy is gypsum used so much in interior partitions?It is different because it is more durable than the rest and it is also:
Has a Light weight.It is sound resistance.One can worked on it even if its wet or dry.Conclusively, the coats of plaster that are used over expanded metal lath are:
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for a given water content, the application of lower compaction energy question 3 options: does not affect the dry unit weight of the soil increases the dry unit weight of the soil decreases the dry unit weight of the soil
For a given water content, the application of lower compaction energy increases the dry unit weight of the soil. So, option A holds the correct answer choice.
Compaction refers to a process that brings about an increase in soil unit weight or density, accompanied by a decrease in air volume. There is usually no change in water content. The degree of compaction is measured by dry unit weight and depends on the water content and compaction effort such as weight of the roller, the number of passes, the number of impacts, and weight of the hammer. So when lower compaction energy is put in, it does not have any effect on the dry unit weight of the soil.
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For (int I=0; I<=10;I++) system.out.println (+','), why is the answer 44?
The code you have provided is a for-loop that prints out the comma character ',' 11 times. The comma character has an ASCII value of 44, so the loop will output 44 11 times. This is why the answer is 44.
The for loop starts at 0 and will continue to run as long as the variable I is less than or equal to 10. Each time the loop runs, the variable I is incremented by 1.
The system.out.println() statement inside the for loop will print out a comma each time the loop runs.
So the output of this code will be 11 commas, like this:
```
,,,,,,,,,,,
```
There is no calculation happening in this code, so the answer is 44. It seems like there may be a mistake or typo in the question.
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What signal propagation phenomena causes the diffusion, or the reflection in multiple different directions, of a signal?
In the radio communication system, multipath is the propagation phenomenon that causes diffusion or reflection in multiple different directions of a signal.
Multipath is a propagation mechanism that impacts the propagation of signals in radio communication. Multipath results in the transmission of data to the receiving antenna by two or more paths. Diffusion and reflection are the causes that create multiple paths for the signal to be delivered.
Diffraction occurs when a signal bends around sharp corners; while reflection occurs when a signal impinges on a smooth object. When a signal is received through more than one path because of the diffraction or reflection, it creates phase shifting and interference of the signal.
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For industrial machinery, straight exposed vertical risers of intermediate metal conduit with threaded couplings are permitted if supported at the top and bottom no more than ___ feet apart.
For industrial machinery, straight exposed vertical risers of intermediate metal conduit with threaded couplings are permitted if supported at the top and bottom no more than 10 feet apart.
As long as they are supported at the top and bottom no more than 10 feet apart, straight exposed vertical risers of intermediate metal conduit with threaded couplings are acceptable for industrial machines. This requirement makes sure that the conduit is stable and well-supported in order to guard against any risks or damage. To ensure compliance and safety when installing industrial gear, it is crucial to follow the precise rules and specifications outlined by local electrical codes and standards.
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When a pungent odor is detected during a sealed system recovery and/or repair which of the following is most likely
Answer: A leak in the system
Explanation:
what could happen if the engine was uncowled during the starting and operating procedures
If an engine fails during rollout or just before takeoff, immediately shut both throttles and land the aircraft safely. Before reaching a safe single engine speed right away after takeoff, drop your nose to increase velocity.
What is the engine starting procedure?Closing the throttle, turning off the fuel pump, setting the mixture control to idle cutoff, and simply cranking the engine is the most reliable hot start method I've found.
What is the procedure for engine failure?If an engine fails during rollout or just before takeoff, immediately shut both throttles and land the aircraft safely. Before reaching a safe single engine speed right away after takeoff, drop your nose to increase velocity. If you are unable to climb, close both throttles and land straight ahead.
What happens if engine fails during take off?The typical practice for the majority of aircraft would be to abandon takeoff if an engine failed during takeoff. In small aircraft, the pilot should turn the throttles down to idle, activate the speed brakes (if provided), and apply the brakes as needed if the engine fails before VR (Rotation Speed).
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According to the sector model of North American city structure, members of low-income groups tend to live in which of the following places
According to the sector model of North American city structure, members of low-income groups tend to live in the central business district (CBD) and the inner-city area.
The sector model of North American city structure is an urban land use model that was created by Homer Hoyt in 1939. It divides a city into a series of sectors that radiate outwards from the CBD. These sectors differ in terms of their socio-economic characteristics and are defined by their level of wealth, housing type, and level of social and economic status.
Land use patterns in the sector model are concentrated around the central business district and expand radially outwards, with the most desirable areas occupying the outermost ring. Members of low-income groups tend to live in the central business district and the inner-city area.
Hence, it can be concluded that according to the sector model of North American city structure, members of low-income groups tend to live in the central business district (CBD) and the inner-city area.
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which zones should you search when approaching an intersection?
You should search the zones to the left and right of your vehicle, as well as any areas directly in front of the intersection, such as crosswalks, bike lanes, and medians. Additionally, you should be aware of any oncoming traffic or pedestrians who may be crossing the intersection.
When approaching an intersection, it is important to pay attention to all of the potential hazards around you. First, you should search the zones to the left and right of your vehicle. This includes looking for oncoming traffic, pedestrians, or cyclists who may be crossing the intersection or entering the roadway. Additionally, you should be aware of any obstacles that may be directly in front of you, such as crosswalks, bicycle lanes, or medians. By taking the time to search all of these zones and be aware of your surroundings, you can increase your safety and the safety of others.
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11) A car manufacturer needs an alarm sound for certain undesirable conditions for the new car. The alarm should be activated when any of the following conditions is met: a) The headlights are on while ignition is off. b) The door is opened while the ignition is off. c) The seat belt is not used when the ignition is on. By using suitable logic gates, design the logic circuit of the alarm system showing all necessary steps. The input variables are as follows: Inputs S D I L Seat belt in use (Input S = 1) All doors are shut (Input D= = 0) Ignition is off (Input I = 1) Headlights are off (Input L = 0) Condition
how to draw logic gates, coding ,kmap and truth table
The fundamental components of any digital system are logic gates. It is an electronic circuit with one or more inputs and just one output.
What is logic gates ?In any digital system, logic gates serve as the fundamental building elements. One or more inputs may be present, but there is only one output in this electronic circuit. An established logic governs the relationship between the input and the output. This is the basis behind the names AND, OR, NOT, etc. given to logic gates.
Using cables that stand for 1s and 0s, we transmit data through computers. In order for computers to someday perform more difficult tasks like computing the 50th digit of, they need to be able to manipulate those 1s and 0s. Input wire 1s and 0s are converted via logic gates in computers.
A K-map is a particular type of truth table that facilitates the mapping of parameter values and leads to a shortened Boolean expression. Functions with two to four variables are ideal candidates for K-maps.
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Calculate the rms value.
Answer:
(√6)/3 ≈ 0.8165
Explanation:
The RMS value is the square root of the mean of the square of the waveform over one period. It will be ...
\(\displaystyle\sqrt{\frac{1}{T}\left(\int_{\frac{T}{4}}^{\frac{3T}{4}}{1^2}\,dt+\int_{\frac{3t}{4}}^{\frac{5t}{4}}{(\frac{-4}{T}}(t-T))^2\,dt\right)}=\sqrt{\frac{1}{T}\left(\frac{T}{2}+\left.\frac{16}{T^2}\cdot\frac{1}{3}(t-T)^3\right|_{\frac{3t}{4}}^{\frac{5t}{4}}\right)}\\\\=\sqrt{\frac{1}{T}\left(\frac{T}{2}+\frac{T}{6}\right)}=\sqrt{\frac{2}{3}}=\boxed{\frac{\sqrt{6}}{3}\approx0.8165}\)
Which is the most common way to install memory in a laptop
Find the cover for the memory module slot. Insert the module by sliding it. The majority of socket alignments are roughly 30 degrees. Change the memory.
What exactly is memory?Memory is the ability to take in information from the surrounding environment, process it, store it, and then recall it at a later time—sometimes years later. A memory storage system or filing cabinet are frequently used as analogies for human memory.
Why is memory so crucial?Memory is a necessary part of every person's life. We are unable to function with in present or consider the future without a remembrance of the past. We wouldn't be able to recall our actions from the previous day, the present, or the future.
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Which of the following is NOT part of a car's drive train?
A axle
B rotor
C differential
D transmission
Answer:
B. rotor
Explanation:
The correct answer Is rotor because the others are part of a cars drivetrain
The drive train system exists as a critical element of a vehicle and the transmission exists as an integral part of the drive train. B rotors NOT part of a car's drive train.
Which is not part of the drive train?A drive train exists not really a single part of your car – it's a set of drive train components that interact with the engine to drive the wheels and different regions of the vehicle to thrust it into motion. These components often contain the transmission, differential, driveshaft, axles, CV joints, and wheels.
Therefore, the correct answer is option B rotors.
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A rigid container is partly filled with a liquid at 1520 kPa. The volume of the liquid is 1.232 litres. At a pressure
of 3039 kPa, the volume of the liquid is 1.231 litres.
a. Calculate the average bulk modulus of elasticity of the liquid
Answer:
Bulk modulus: ß = - ∆p/(∆V/V)
∆p = (3039 - 1520)x10³ = 1519 kPa
∆V = 1231 - 1232 = -1 m³
V = 1232 m³
ß = - 1519/(-1/1232) = 1.87x10^6 kPa = 1.87 GPa
Explanation:
a.The average bulk modulus of elasticity of the liquid is 1.87 GPa
b. Coefficient of compressibility 0.5437 GPa-¹
c Velocity of sound 1.87 x 10^9P
a. Bulk modulus of elasticity
ß = - ∆p/(∆V/V)
First step is to determine ∆p
∆p = (3039 kpa - 1520 kpa)x10³
∆p = 1519 kPa
Second step is to determine ∆V
∆V = 1231 litres - 1232 litres
∆V = -1 m³
Now let determine the Bulk modulus of elasticity
Bulk modulus of elasticity= - 1519/(-1/1232)
Bulk modulus of elasticity= 1.87x10^6 kPa
Bulk modulus of elasticity= 1.87 GPa
b. The coefficient of compressibility
Coefficient of compressibility=β =1/K
Coefficient of compressibility=β =1/1.87
β =0.5437 GPa-¹
C. Velocity of sounds in the medium with a density of 1593 kg/m3
V=√K/ρ
V=√1.87×10^9/ 1593
V=1083m/s
V = 1.87 x 10^9P
Inconclusion:
a.The average bulk modulus of elasticity of the liquid is 1.87 GPa
b. Coefficient of compressibility 0.5437 GPa-¹
c Velocity of sound 1.87 x 10^9P
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Pre-lab Assignment: "Use the introduction and experimental procedure to answer the following questions." 1. Complete the flowchart below by naming the appropriate physical separation technique onto the lines provided. 2) How does one calculate the mass of the sample? [0.5] 3) How does one calculate the mass of the rice? [0.5] 4) How does one calculate the mass of the sand? [0.5] 5) How does one calculate the mass of the salt? [0.5] 6) How does one calculate the percentage of each component in the mixture?
The questions in the pre-lab assignment focus on various aspects of the experiment, including physical separation techniques, calculation of sample mass, and determination of component percentages.
Step 1: The appropriate physical separation techniques to complete the flowchart could include methods such as filtration, evaporation, and magnetic separation, depending on the specific requirements of the experiment. These techniques are used to separate the different components of the mixture based on their physical properties.
Step 2: To calculate the mass of the sample, one typically weighs the entire mixture before performing any separation steps. This measurement provides the initial mass of the mixture, which serves as a reference for subsequent calculations.
Step 3: The mass of the rice can be determined by isolating the rice component through a suitable separation technique and weighing the collected rice. The difference between the initial mass of the mixture and the mass of the other components will represent the mass of the rice.
Step 4: Similarly, the mass of the sand can be calculated by separating the sand from the mixture and weighing it. The difference between the initial mass and the mass of the remaining components will correspond to the mass of the sand.
Step 5: To determine the mass of the salt, the salt component needs to be separated from the mixture and weighed. The difference between the initial mass and the masses of the other components will indicate the mass of the salt.
Step 6: The percentage of each component in the mixture can be calculated by dividing the mass of each component by the initial mass of the mixture and multiplying by 100. This calculation provides the proportion of each component relative to the total mass of the mixture.
By addressing these questions, students gain a better understanding of the experimental procedure, the use of physical separation techniques, and the importance of accurately calculating masses and percentages in the context of the experiment.
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4. A cylindrical specimen of a brass alloy 7.5 mm in diameter and 90.0 mm long is pulled in tension with a force of 6000 N; the force is subsequently released. a. Compute the final length of the specimen. b. Compute the final specimen length with the load is increased to 16,500 N and then released.
The elastic properties of the brass specimen enables it to return to its
original length when stressed below the yield strength.
The correct responses are;
4. a. The final length is 90.0 m.
b. The final length is 97.2 mm.
Reasons:
a. Diameter of the brass alloy = 7.5 mm
Length of the specimen = 90.0 mm
Force applied = 6000 N
The equation for the applied stress, σ, is presented as follows;
\(\sigma = \dfrac{Force \ applied}{Area \ of \ specimen} = \dfrac{6000 \, N}{\pi \cdot \left(\dfrac{7.5 \times 10^{-3}}{2} \, m} \right)^2 } \approx 135.81 \ \mathrm{MPA}\)
Depending on the cold working condition, 135.81 MPa is below the yield
strength, and the brass will return to its original condition when the force is
removed. The final length is remains as 90.0 m.
b. When the applied force is F = 16,500 N, we have;
\(\sigma = \dfrac{16,500\, N}{\pi \cdot \left(\dfrac{7.5 \times 10^{-3}}{2} \, m} \right)^2 } \approx 373.48\ \mathrm{MPA}\)
The stress found for the force of 16,500 N is above the yield stress of
brass, and it is therefore, in the plastic region.
From the stress strain curve, the strain can be estimated by drawing a line
from the point of the 373.48 MP on the stress strain curve, parallel to the
elastic region to intersect the strain axis, which gives a value of strain
approximately, ε = 0.08.
The length of the specimen is given by the formula; \(l_i = l_0 \cdot (1 + \epsilon)\)
Therefore;
\(l_i\) = 90 × (1 + 0.08) = 97.2
The final length of the specimen, \(l_i\) = 97.2 mm
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To measure an object accurately, what point on the ruler would you align with the object edge
Answer:
Along the zero to measure an object on a ruler
Which values are marked for deallocation after the sequence? Integer obji = new Integer(10); Integer obj2 = new Integer (28); Integer obj3 =. 0bj2; Integer obj4 = new Integer (40); obj2 = null; oobj4 = 0bj1;
The garbage collector can deallocate the Integer object with the value 28 since it no longer has any references pointing to it. Likewise replaced is the reference to the Integer object with the value 40.
Which Java data type is invalid?However in Java, unlike C/C++, short int and long int are invalid data types. Moreover, Java does not distinguish between signed and unsigned in any way.
What are the 5 types of data?The five fundamental data types that are supported by the majority of modern computer languages are Integral, Floating Point, Character, Character String, and Composite types. A number of specific subtypes are also included in each general group.
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When handling chemicals and solvents, technicians are recommended to
Answer:
To wear PPEHave prior knowledge of explosive levels and elemental propertiesKnow procedure to eliminate any threatAnswer
have PPE on wash hands after
Explanation:
what is the magnetic field strength in the air-core of a solenoid
Answer:The magnetic field in a solenoid formula is given by, B = μoIN / L B = (1.26×10−6 × 15 × 360) / 0.8 B = 8.505 × 10−3 N/Amps m
Explanation:
The magnetic field generated by the solenoid is 8.505 × 10−4 N/Amps m.
What is the maximum width for most vehicles?
What are the initial questions that a systems analyst must answer to build an initial prototype of the system output.
Consider a unity feedback system with: G(s) = (K(s+1))/(s^2 + 4s + 5) a). Find the angle of departure of the root locus from the complex poles. b). Find the break-in point for the root locus as it enters the real axis.
A) Angle of departure The angle of departure of a root locus from a complex pole pair is given by: \($$\theta = 180^\circ - \phi_p - \phi_z$$\)$$\theta = 180^\circ - \phi_p - \phi_z$$
where θ is the angle of departure, φp is the phase angle at the pole, and φz is the phase angle at the zero. From the transfer function given, we can find the complex poles as follows:
$$(s+2)^2 + 1^2 = 0$$$$\
implies s = -2 \pm j$$At these poles, the phase angle is given by:
\($${\rm \phi_p} = tan^{-1}\left(\frac{-Im}{Re}\right) = tan^{-1}\left(\frac{-1}{-2}\right) = 26.6^\circ$$\)
The angle of departure is therefore:
\($$\theta = 180^\circ - 26.6^\circ - 0^\circ = 153.4^\circ$$B)\)
Break-in pointThe break-in point is the point where the root locus enters the real axis. It occurs when the real axis is a part of the locus and lies between two real poles or real zeros.
For a second-order system, the break-in point occurs when the angle of departure and the angle of arrival to the real axis are equal.In this case, we can see that there are no real zeros or real poles, so the locus cannot enter the real axis.
Therefore, there is no break-in point for this system.
\($$G(s) = \frac{K(s+1)}{s^2 + 4s + 5}$$a)\)The angle of departure of the root locus from the complex poles is \($$153.4^{\circ}$$b)\) The root locus does not enter the real axis, so there is no break-in point.
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