Simplify this simple series/parallel circuit into one
(1) resistor connected to the 220Vdc source. Use
Ohm's Law to solve for the voltage across the
resistors that have voltmeters attached, as well as
the currents through resistors that have ammeters
attached. Use Watt's Law to calculate power
consumed in the specified resistors.
Answers
In order to simplify a series/parallel circuit and ascertain the voltage dispersed across the resistors utilizing voltmeters, follow these guidelines:
Guidelines to use:Identify concurrent relationships - either sequential or parallel in the current transmission. Calculate the equalizing resistance for each proportionate sequential and proportional equivalent individually.
Use computational methods to calculate the comprehensive equivalent resistance spanning throughout the entire conduit. Determine the cumulative intensity flowing through the confined area.
Utilize Ohm's Law to determine volts per resistor by means of an indicator-voltmeter approach.
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Related Questions
When the Accident Prevention Department is working at full capacity, occupational accidents should become insignificant to an organization seeking to achieve its competitive advantage.
Do you agree or disagree?
Answers
I disagree with the statement that when the Accident Prevention Department is working at full capacity, occupational accidents should become insignificant to an organization seeking to achieve its competitive advantage.
The Accident Prevention Department is a section of the organization that focuses on implementing safety and health guidelines to decrease the likelihood of accidents occurring. The objective of the Accident Prevention Department is to eliminate the root causes of accidents and ensure a safe and healthy work environment for employees. While the department is not entirely responsible for preventing accidents, it is in charge of overseeing and managing the organization's safety and health initiatives, policies, and regulations.What does an organization's competitive advantage mean?Competitive advantage refers to the unique advantage a company has over its rivals. This advantage enables the organization to gain market share, increase revenue, and enhance its brand image. An organization's competitive advantage can be based on a variety of factors, including innovation, pricing, customer service, product quality, and brand image. The advantage can either be tangible or intangible.Why do I disagree with the statement?The statement claims that when the Accident Prevention Department is functioning at full capacity, occupational accidents should become insignificant to an organization looking to achieve a competitive advantage. However, this statement is not completely valid because although the Accident Prevention Department may be able to reduce the number of accidents that occur in an organization, accidents can still occur.Therefore, regardless of how well an organization's Accident Prevention Department performs, it cannot entirely eliminate the chance of occupational accidents occurring. Therefore, the organization must continue to address potential safety hazards and provide comprehensive training to employees to minimize the risk of accidents and achieve a competitive advantage.
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Toyotas more than 30 hybrid vehicles investment in zero emissions vehicle and working on developing hydrogen fuel cell vehicles not only protect the natural environment but also further his overall economic progress customer is generally has positive feelings towards companies that focus on______ efforts such as Toyotas
Answers
The missing term in the presented paragraph is environmental.
In recent years the effects of climate change have been strongly manifested around the world causing:
Forest firesFloodsHeatwavesCold wavesSnowfallThe rise in the level of rivers and seasDeglaciationTherefore, many companies have begun to investigate productive alternatives to reduce their environmental impact. In the case of the car industry, companies have deepened their research on other sources of energy such as:
ElectricSolarWindOne of them is Toyota, the Japanese brand that has developed cars that work hybrid, that is, with gasoline and electric power. This will reduce the emissions of CO2 and other harmful gases into the atmosphere.
Therefore, it is possible to infer that the missing term in the paragraph is Environmental.
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Question #9
Multiple Choice
Which statement characterizes how the creation of LIMBS benefits developing countries?
O Using nanotechnology, a new material is created to benefit many other products
Using only natural materials, there is little chemical production, thus reducing the pollution in these countries
Using regional materials creates a sustainable program that breaks countries dependencies on other nations
Using fabricated materials, no natural resources are overfarmed, keeping the environment intact.
© 2014 Glynlyon, Inc.
Answers
Answer:
Using regional materials creates a sustainable program that breaks countries’ dependencies on other nations.
Explanation:
i did the assignment
Answer:
Using regional materials creates a sustainable program that breaks countries’ dependencies on other nations.
Explanation:
C
Storing past experiences in the form of cases is a KM method called ________.
A. case-based reasoning (CBR)
B. knowledge approach (KA)
C. case-based approach (CBA)
D. knowledge-based reasoning (KBR)
E. knowledge reasoning (KR)
Answers
The correct answer to the question is A. case-based reasoning (CBR). This knowledge management (KM) method involves storing past experiences or cases in a knowledge base that can be accessed and reused to solve new problems or make decisions. CBR is an artificial intelligence technique that uses the principles of similarity and analogy to retrieve relevant cases and adapt them to new situations. It is a valuable KM approach because it allows organizations to leverage the collective knowledge and expertise of their employees, and to capture and retain institutional knowledge that might otherwise be lost. CBR can also improve organizational learning, decision-making, and problem-solving by enabling individuals to learn from past experiences and apply this knowledge to new challenges. Overall, CBR is a powerful KM method that can help organizations to optimize their knowledge assets and to continuously improve their operations and performance.
which of these is a term for a person who does not share the belief of the dominant religion of a society ?
A. a heathen
B. Assimilated
C. Uncivilized
D. A savage
Answers
Answer: a heathen
Explanation:
The term for a person who does not share the belief of the dominant religion of a society is "a heathen". The correct option is A.
What is society?A society is a group of people who interact with one another on a regular basis, or a large social group that shares the same spatial or social territory and is typically subject to the same political authority and dominant cultural expectations.
"A heathen" is a person who does not share the beliefs of a society's dominant religion.
The term is frequently used to describe someone who is considered uncivilized or primitive because of their religious beliefs, especially in societies where the dominant religion wields significant power and influence.
However, it is important to note that the term can be considered derogatory and offensive, and it is generally more respectful to refer to people of different religious beliefs using neutral or positive terms.
Thus, the correct option is A.
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Describe the extent of their own responsibility. When to act on their own innitiative to find , clarify and evaluate information , and to whom they should report if they have problems they cannot resolve in the work place
Answers
Answer:
whatsthe question choices
What action control to move the rudder from one point to the other?
Answers
The action control to move the rudder from one point to the other is doen when The rudder, when turned to starboard, produce a force that is towards the port (called the rudder force).
What controls the rudder of a ship?In a vessel or ship, found in small craft, the rudder is known to be operated manually through the use of a handle that is called a tiller or helm.
In a bigger vessels, the rudder is known to be turned through the use of an hydraulic, steam, or electrical machinery. The first type of rudder was side to be a paddle or oar.
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Find the value of P(-1.5≤Z≤2)
Answers
Answer:
0.9104
Explanation:
Suitable technology can tell you the probability.
P(-1.5≤Z≤2) ≈ 0.9104
__
A phone app gives the probability as 0.9104426667829628.
a fault is an example of a. brittle deformation b. ductile deformation c. elastic deformation d. all of the above
Answers
The correct answer is a. brittle deformation. therefore the correct option is (a) option.
Brittle deformation is when rocks fail as rigid solids. The rocks will break, rather than bend, under these conditions to produce fractures. Brittle deformation occurs along discrete planes in the rock instead of involving the rock body as a whole.Brittle materials include glass, ceramic, graphite, and some alloys with extremely low plasticity, in which cracks can initiate without plastic deformation and can soon evolve into brittle breakage.
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Con una tasa de interés de 8% por año, ¿a cuánto equivalen $10 000 de hoy, a) dentro de un año, y b) hace un año?
Answers
Answer:
que hces en eeuua
Explanation:
Diseña un mecanismo multiplicador con un engranaje motriz cuya relación de transmisión sea de 0.5 y que transmita el movimiento entre ejes distantes. Inserta una captura de pantalla indicando la relación entre los diámetros y la velocidad de giro del engranaje motriz.
Answers
You leave your house at 5:02 PM and run 20 yards down the street. You don't realize that you forgot your Wallet back at home and turn around. You have run a third of the way back when you look at your watch and see that it change to say 5:03 PM. What is your average velocity in m/s up to this point
Answers
Answer:
The average velocity is 0.203 m/s
Explanation:
Given;
initial displacement, x₁ = 20 yards = 18.288 m
final displacement, x₂ = ¹/₃ x 18.288 = 6.096 m
change in time between 5:02 PM and 5:03 PM, Δt = 3 mins - 2 mins = 1 min = 60 s
The average velocity is given by;
V = change in displacement / change in time
V = (x₂ - x₁) / Δt
V = (18.288 - 6.096) / 60
V = 0.203 m/s
Therefore, the average velocity is 0.203 m/s
What quantity measures the effect of change?
control variable
independent variable
relative variable
dependent variable
Answers
Answer:
The Dependent Variable is the Effect, Its value depends on changes from the Independent Variable
Hope this Helps
Avapor mixture containing 50.0 mole % benzene and 50.0 mole % toluene at 1 atm is cooled isobarically in a closed container from an initial temperature of 115°C. Use the Tsy diagram below to answer the following questions. 115 110 1400 1300 105 100 Vapor 1200 95 Temperature (°C) 90 Liquid 1100 1000 900 Pressure (mm Hg) Liquid 85 800 Vapor 80 700 75 70 600 500 0 1.0 65 0 10 0.2 0.4 0.6 0.8 Mole fraction henvene Polarm 0.2 0.4 0.6 0.8 Mole fraction benzene 7100 First Condensation Your answer is partially correct. At what temperature does the first drop of condensate form? 104 °C What is its composition? 0.20 mol benzene/mol
Last Condensate Your answer is partially correct. At what temperature does the last bubble of vapor condense? °C 98 What is its composition? 0.53 mol benzene/mol
Answers
Answer:
105°touch sensce what I could wathskb
Which of the following would most likely be associated with the word disposal? answer choices. a. rotten food. b. basic needs. c. extra supplies. d. opposing ideas
Answers
The term most likely to be associated with the word disposal is:
a. rotten food
Rotten food is typically something that needs to be disposed of, as it is no longer safe or suitable for consumption.
Disposing of rotten food properly is important to avoid the spread of bacteria and unpleasant odors. Here are some guidelines for disposing of rotten food:
Inspect the food: Check your fridge, pantry, or wherever you store food for any items that have spoiled or gone bad. Look for signs like mold, foul smell, or an unusual textureSeparate rotten food: Remove the rotten food from any other items to prevent cross-contamination. Use gloves or utensils to handle the spoiled items, and place them in a designated container or bagSeal the container: Close the container tightly to contain the smell and prevent any leakage. If the food is particularly odorous, consider double-bagging it or using an airtight containerTrash disposal: Dispose of the sealed container in your regular trash bin. If possible, try to put it in an outdoor trash bin to minimize the smell inside your home. If you have composting facilities or organic waste collection in your area, check if the rotten food can be composted insteadClean the area: After removing the rotten food, thoroughly clean the area where it was stored. Use a mild detergent or disinfectant to sanitize the surfaces and eliminate any lingering odorsPrevent future spoilage: To reduce the chances of food going bad in the future, practice good food storage habits. Check expiration dates, store perishable items at appropriate temperatures, and use airtight containers to maintain freshness.To know more about waste management, visit the link : https://brainly.com/question/28003333
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A resistor has code 104 printed on it .What is the resistive value of this resistor
Answers
Answer:
X = 1 (1st digit in the code)
Y = 0 (2nd digit)
Z = 4 (3rd multiplier digit)
104 → 10 × 10^4 Ω
→ 10 × 10000Ω
→ 100 kΩ
resistors are marked 104, 105, 205, 751, and 754. The resistor marked with 104 should be 100kΩ (10x10^4), 105 would be 1MΩ (10x10^5), and 205 is 2MΩ (20x10^5). 751 is 750Ω (75x10^1), and 754 is 750kΩ (75x10^4).
Here we need to understand how a code in a resistor gives us information on the resistor. Here we will see that the code means that the resistance is 100,000 Ω.
When we use numbers, let's assume that we have 3 single-digit numbers abc.
So if the code in our resistor is abc, this will mean that the resistance of the resistor is:
ab×10^c Ω
Using this general rule we can see that if the code is 104, then the resistance will be:
r = 10×10^4 Ω
= 100,000 Ω
Then we can conclude that the resistive value of this resistor is 100,000 Ω
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1. What is the primary goal of penetration testing? a. Attempt to uncover deep vulnerabilities and then manually exploit them b. Scan a network for open FTP ports c. Perform SYN DOS attack towards a server in a network d. Attempt to perform an automated scan to discover vulnerabilities
2. There is often confusion between vulnerability scanning and penetration testing. What is the best explanation of the difference between vulnerability scanning and penetration testing? a. Vulnerability scanning is performed using an automated tool to scan a network known vulnerability signatures. Penetration testing involves attempting to manually uncover deep vulnerabilities just as a threat actor would, and then exploiting them. b. Vulnerability scanning checks a network for outdated versions of services. Penetration testing is attempting to manually uncover deep vulnerabilities just a threat actor would, and then exploiting them. c. Vulnerability scanning is performed by manually scanning a network for known vulnerabilities. Penetration testing is attempting to manually scan a network for known vulnerability signatures using an advanced scanning tool. d. Vulnerability scanning checks a network for open ports and services. Penetratic testing is attempting to manually scan a network for known vulnerability signatu using an advanced scanning tool. 3. Khalid joins a security team where he is assigned an SOC developer role and has to build different teams under SOC. Which of the following teams should he build to deal with providing real-time feedback related to security incidents and threat detections, which can then be utilized to facilitate better prioritization of threats and a mature way of detecting threats? a. Red team b. Blue team c. Purple team d. White team
Answers
1) Note that the primary goal of penetration testing is to 2Attempt to uncover deep vulnerabilities and then manually exploit them" (Option A)
2) The best explanation for the difference between vulnerability scanning and penetration testing is; "Vulnerability scanning is performed using an automated tool to scan a network known vulnerability signatures. Penetration testing involves attempting to manually uncover deep vulnerabilities just as a threat actor would, and then exploiting them." (Option A)
3) Given the above scenario, the team that he should build to deal with providing real-time feedback related to security incidents and threat detections, which can then be utilized to facilitate better prioritization of threats and a mature way of detecting threats is "the Purple Team" (Option C).
Why is Penetration Testing Important?The major reason penetration testing is important for an organization's security is that they teach staff how to deal with any form of hostile entity break-in. Pen tests are used to determine whether a company's security practices are truly effective.
Some compliance rules require penetration testing. Aside from that, you should conduct regular pentests to analyze and upgrade your security procedures against cyberattacks.
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There is a moving sidewalk at the airport that is often broken. It is 87 m long. When it is broken you can walk the full length in 106 seconds. When it is working and you ride without walking, the ride for the full length takes 66 sec. When it is working and you walk as you ride, you walk at the same pace as before. A. Sketch all 3 scenarios labeling all velocities as though you were standing in the airport watching people on the moving sidewalk. B. How fast are you traveling when the sidewalk is broken? C. How fast are you traveling when you just ride the sidewalk? D. How fast are you moving and how long will it take you to travel the full length if you walk while riding the moving sidewalk? Assume you walk at the same speed as when it is broken.
Answers
The correct answer is A.Scenario 1: Broken SidewalkPerson's velocity = walking velocity, opposite direction of the sidewalk's directionScenario 2: Riding SidewalkPerson's velocity = sidewalk's velocity.
same direction as the sidewalk's directionScenario 3: Walking and Riding SidewalkPerson's velocity = (walking velocity + sidewalk's velocity), same direction as the sidewalk's directionWhen the sidewalk is broken, the person's velocity is equal to their walking velocity. Therefore, to find the person's velocity, we need to divide the length of the sidewalk by the time it takes to walk the full length:velocity = distance/time = 87m/106s = 0.82 m/sWhen the person is just riding the sidewalk without walking, their velocity is equal to the velocity of the sidewalk itself. Therefore, we can use the same equation as in part B, but with the different time:velocity = distance/time = 87m/66s = 1.32 m/sWhen walking and riding the sidewalk at the same time, the person's velocity is the sum of their walking velocity and the sidewalk's velocity
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Some_____
include peanut butter, bacon, and chocolate.
Snap traps baits
Glue boards
Catchalls
IGRs
Bait stations
Answers
Answer:
it’s IGS
Explanation:
because i read
Answer:
snap trap baits
Explanation: its kind of obvi, but i took the test and got it right.
when applying an acrylic overlay, think of the nail as divided into how many zones?
Answers
Acrylic overlay is a popular technique used by nail technicians to give a protective layer to the natural nail or enhance the appearance of the nails. It involves applying a mixture of liquid and powder acrylic on the nails, which hardens to create a durable and long-lasting coating.
When applying an acrylic overlay, the nail is typically divided into three zones: the free edge, the stress area, and the nail bed. The free edge is the tip of the nail that extends beyond the fingertip, the stress area is the middle section of the nail that experiences the most pressure and tension, and the nail bed is the area closest to the cuticle. The free edge is the zone where the acrylic is applied the thinnest, usually just a thin layer of clear acrylic to protect the natural nail. The stress area is where most of the acrylic is applied, creating a thicker layer to provide strength and durability. The nail bed is the zone where the acrylic is applied the thickest, often in a light pink shade to create a natural-looking base for nail polish.
In conclusion, when applying an acrylic overlay, the nail is typically divided into three zones: the free edge, the stress area, and the nail bed. This division allows the nail technician to apply the acrylic in a way that provides maximum protection and durability while still creating a natural-looking finish.
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The seven P's adds _____.
Answers
The seven P's adds people , place , physical and process. Moreover, these seven elements comprise the marketing mix.
What are the seven Ps?Every part of your marketing strategy can benefit from using the 7Ps of marketing. To ensure that you are conveying a coherent and consistent message about your business and brand, you should take into account the product, price, location, promotion, people, process, and physical evidence holistically.
Why are the 7 Ps important?The 7Ps help businesses examine and define key issues that influence product and service marketing. The marketing mix, also known as the 7Ps framework for the digital marketing mix, which is a well-liked marketing model.
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A liquid stream containing 50. 0 mole% benzene and the balance toluene at 25°C is fed to a continuous single-stage evaporator at a rate of 1320 mol/s. The liquid and vapor streams leaving the evaporator are both at 95. 0°C. The liquid contains 42. 5 mole% benzene and the vapor contains 73. 5 mole% benzene. (a) Calculate the heating requirement for this process in kW. (b) Using Raoult's law (Section 6. 4b) to describe the equilibrium between the vapor and liquid outlet streams, determine whether or not the given benzene analyses are consistent with each other. If they are, calculate the pressure (tor) at which the evaporator must be operating; if they are not, give several possible explanations for the inconsistency
Answers
(a) The heating requirement for this process is 2.95 x 10⁶ kW
(b) The given benzene analyses are not consistent with each other.
(a) To calculate the heating requirement for this process, we need to determine the heat that must be supplied to the evaporator to vaporize the liquid stream and heat the vapor to the outlet temperature of 95.0°C. We can use the following energy balance:
Q = m(L)v + m(V)h
where Q is the heat required, m(L) and m(V) are the mass flow rates of the liquid and vapor streams, respectively, and v and h are the specific volumes and enthalpies of the liquid and vapor streams, respectively.
To convert the given mole fractions to mass fractions, we need to use the molecular weights of benzene and toluene:
MW_benzene = 78.11 g/mol
MW_toluene = 92.14 g/mol
The mass fraction of benzene in the liquid stream is:
y_B = 0.50
M_B = y_B x MW_benzene / ((1 - y_B) x MW_toluene + y_B x MW_benzene) = 0.436
Similarly, the mass fraction of benzene in the liquid outlet stream is:
x_B = 0.425
M_B = x_B (MW_benzene) / ((1 - x_B) MW_toluene + x_B ( MW_benzene) = 0.378
And the mass fraction of benzene in the vapor stream is:
z_B = 0.735
M_B = z_B x MW_benzene / ((1 - z_B) x MW_toluene + z_B x MW_benzene) = 0.532
Now we can use Raoult's law to relate the vapor pressures of benzene and toluene in the liquid and vapor streams:
P_B = y_B x P°_B
P_T = (1 - y_B) x P°_T
P'_B = z_B x P°_B'
P'_T = (1 - z_B) x P°_T'
where P°_B and P°_T are the vapor pressures of pure benzene and toluene at 25°C, and P°_B' and P°_T' are the vapor pressures of pure benzene and toluene at 95°C. We can look up these values in a reference table:
P°_B = 12.7 kPa
P°_T = 3.8 kPa
P°_B' = 95.4 kPa
P°_T' = 12.6 kPa
Substituting these values and solving for the vapor pressure of benzene in the liquid and vapor streams, we get:
P_B = 6.35 kPa
P'_B = 50.80 kPa
Now we can calculate the mass flow rates of the liquid and vapor streams:
m(L) = 1320 / (1 + V/L)
m(V) = 1320 - m(L)
where V/L is the ratio of the vapor flow rate to the liquid flow rate, which we can calculate from the vapor-liquid equilibrium relation:
V/L = z_B / (y_B - z_B) = 1.53
Substituting these values and the specific volumes and enthalpies of benzene and toluene, which we can look up in a reference table, we get:
v_L = 0.001319 m³/mol
v_V = 0.03147 m³/mol
h_L = -15702 J/mol
h_V = -11006 J/mol
Q = m(L)v_L(h_V - h_L) + m(V)h_V
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explain ten application of solar electric energy
Answers
Answer:
Some of the major application of solar energy are as follows: (a) Solar water heating (b) Solar heating of buildings (c) Solar distillation (d) Solar pumping (e) Solar drying of agricultural and animal products (f) Solar furnaces (g) Solar cooking (h) Solar electric power generation (i) Solar thermal power production (j) Solar green houses.
The IRT has a vital responsibility in gathering forensic evidence, which is defined as collecting and preserving the information that can be used to reconstruct events.
a. True
b. False
Answers
The yield stress for a zirconium-magnesium alloy is σY = 15. 3 ksi. A machine part is made of this material and a critical point in the material is subjected to in-plane principal stresses σ1 and σ2 = −0. 54 σ1.
Determine the magnitude of σ1 that will cause yielding according to the maximum-shear-stress theory
Answers
The magnitude of σ1 that will cause yielding according to the maximum-shear-stress theory is 9.94 ksi.
Yield stress for the zirconium-magnesium alloy, σY = 15.3 ksi
In-plane principal stresses are σ1 and σ2 = −0.54σ1
To find the maximum shear stress theory, the equation used is τ_max=1/2(σ1-σ2)
The maximum shear stress theory states that yielding begins when the maximum shear stress in a part equals or exceeds the shear strength of the material. It is represented as τ_max = τ_yield
Where τ_max is the maximum shear stress in a part and τ_yield is the shear strength of the material. In-plane principal stresses are σ1 and σ2 = −0.54σ1
Let us replace the value of σ2 in terms of σ1σ2 = −0.54σ1,σ1 = 1.85σ2
Substitute the values in the τ_max=1/2(σ1-σ2)
τ_max=1/2(σ1-(-0.54σ1))
τ_max=0.77σ1
Now, τ_yield= σY/2 = 7.65 ksi
Therefore, 0.77σ1 = 7.65
σ1 = 9.94 ksi
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A basic 3-input logic circuit has a LOW on one input and a HIGH on the other two inputs, and the output is LOW. What type of logic circuit is it
Answers
Answer:
any of AND, NOR, XOR
Explanation:
An AND gate will give a Low output for any input Low. The logic circuit could be an AND gate.
A NOR gate will give a Low output for any input High. The logic circuit could be a NOR gate.
An XOR gate will give a Low output for an even number of High inputs. The logic circuit could be an XOR gate.
The logic circuit could be any of ...
AND or NOR or XOR
__
Additional comment
What you consider a "basic" gate is not defined here. All of these are catalog items. If you consider only AND, OR, and NOT to be the basic gates, then your answer is AND.
I want to know if anyone else know how to tell apart real leather from fake leather?!?!
Answers
Answer:
yes i do.
Explanation:
it's pretty easy in my opinion but i dont know about you why do you ask?
Pls help and solve this problem
Answers
Dynamics of Rigid Bodies:
Problem 1) A car is moving with constant acceleration covers 450 m in a 5 second interval and further it covers 700 m in a 10 second interval. What is the acceleration of the car?
Given:
D/S1= 450 m Total Distance = 450+700 = 1150
T1= 5 seconds
Distance/S2=700m
T2= 10 seconds
when car covers 450m
Formula: ( S=ut + 1/2 at^2)
450m = 5u + 1/2 x a x (5)^2
450m = 5(-5a+1150)+1/2 a (25)
450m = -25+ 575 + 25/2
-575+450=-25/2 a
-125 = -12.5 a
a = +10 m/s^2
Get the value of u :
1150 = 10u + 1/2 x a x (10)^2
1150 = 10u + 1/2 x a x 100
1150 = 10u + 50a
-10u= 50 a - 1150
10u/50a= -1150
u = -5 +1150
Answers
Answer:
The acceleration of the car is +10 m/s^2.
Explanation:
Using the formula S = ut + 1/2at^2, we can calculate the acceleration of the car.
When the car covers 450 m in 5 seconds, we have:
450 = 5u + 1/2 x a x 5^2
Simplifying this equation gives us:
450 = 5u + 12.5a
Next, when the car covers a total distance of 1150 m in 15 seconds, we have:
1150 = 10u + 1/2 x a x 10^2
Simplifying this equation gives us:
1150 = 10u + 50a
We can now solve for u in terms of a using the first equation:
5u = 450 - 12.5a
u = (450 - 12.5a)/5
Substituting this expression for u into the second equation gives:
1150 = 2(450 - 12.5a) + 50a
Simplifying and solving for a gives:
a = 10 m/s^2
Therefore, the acceleration of the car is +10 m/s^2.
Suppose we have a rod of length n inches and we also have an array of prices P, where P[i] denotes the selling price ($) of a piece that is i inches long. In class, we introduced an algorithm that uses dynamic programming to find a way of cutting the rod into pieces that maximizes the revenue (See CLRS Ch15.1 for reference). Suppose now we have to pay a cost of $1 per cut. The profit can be defined as revenue minus the total cost of cutting. Suggest an algorithm to find a way to cut the rod that maximizes our profit. State a expression for the run time of your algorithm.
Answers
The optimal solution to our problem as the set of cuts that maximizes the profit, which is revenue minus the total cost of cutting. The algorithm is based on a dynamic programming approach, which solves the problem using an iterative approach.
The cutting option which maximizes the profit for that step. The total runtime of this algorithm is \(O(n^2)\), where n is the length of the rod.
Assume we have n=8 inches long rod and P=[1,5,8,9,10,17,17,20] as an array of prices for i-inch rods.
At the very first iteration (for a 1-inch rod), revenue will be P[1] which is 1.At the second iteration (2-inch rod), revenue will be max(P[2], revenue[1]+revenue[1]) which is max(5, 1+1) which is 2.In the 3rd iteration (3-inch rod), revenue will be, max(P[3], revenue[2]+revenue[1]) which is max(8,2+1) which is 3. Similarly, in the nth iteration (n-inch rod), the revenue will be revenue[n] = max(P[i], revenue[n-i]+revenue[i]) for 'i' in range(1, n+1). The above algorithm takes O(n^2) time to get revenue.Now, to maximize the profit, we have to minimize the number of cuts. Let's say, we need x cuts to get the maximum revenue.
Then, the total cost of cutting will be x*cost = x.
So, the profit will be, profit = revenue - cost = revenue - x.
Now, we need to find the number of cuts which will minimize the total cost. Since we already know the revenue with Dynamic Programming, we can now check the minimum number of cuts to get the maximum revenue.
Following is the algorithm to minimize the cuts to maximize the profit: min_cuts[1] = 0 for 'j' in range (2,n+1): min_cuts[j] = 999999 for 'i' in range(1,j+1):
If, revenue[i] + revenue[j-i] - 1 < revenue[j]: continue if, min_cuts[j] > min_cuts[i-1] + min_cuts[j-i] + 1: min_cuts[j] = min_cuts[i-1] + min_cuts[j-i] + 1
Here, the first for loop is for the Dynamic Programming approach (to find revenue), and the second for loop is to minimize the number of cuts to maximize the profit.
The above algorithm will take \(O(n^2)\) time to minimize the cuts. Therefore, the expression for the run time of the above algorithm is \(O(n^2)\).
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