if vertex-cover is intractable, can we conclude that independent-set is intractable?
Answers
We cannot directly conclude that the independent-set is intractable just because the vertex-cover is intractable. These two problems are different and may have different levels of difficulty.
While vertex-cover is the problem of finding the smallest set of vertices that covers all edges in a graph, independent-set is the problem of finding the largest set of vertices with no edges between them. However, there is a relationship between these problems known as complementarity. This means that the complement of an independent set is a vertex cover and vice versa. Therefore, if we can solve one of these problems in polynomial time, we can solve the other in polynomial time as well. However, if one of these problems is intractable, we cannot conclude the same for the other without further analysis.
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Related Questions
A student places a piece of a potato into a container of hydrogen peroxide. One observation the student makes is that bubbles form around the potato. The presence of bubbles might indicate the formation of a new substance because bubbles
a - Group of answer choices always rise to the top of a liquid.
b- are almost always perfectly spherical.
c- could show that a gas is forming.
d- usually burst after a few minutes.
Answers
A student used a 500-ml graduated cylinder to measure the volume of water in a 1-cup measure. three trials of the measurement gave volumes of 240 ml, 242 ml, and 235 ml. What is the average of the three measurements?
Answers
Answer:
239 mL
Explanation:
The average of any set of data is the sum of the values, divided by their number.
v = (240 +242 +235)/3 = 717/3 = 239 . . . mL
The average of the three measurements is 239 mL.
If the sum of the two numbers is 4 and the sum of their squares minus three times their product is 76,find the number
Answers
Answer:
-2 and 6
Explanation:
Let "x" and "y" be 2 numbers.
The sum of the two numbers is 4. The mathematical expression is:
x + y = 4
y = 4 - x [1]
The sum of their squares minus three times their product is 76. The mathematical expression is:
x² + y² - 3 x y = 76 [2]
If we substitute [1] in [2], we get:
x² + (4 - x)² - 3 x (4 - x) = 76
x² + 16 - 8 x + x² - 12 x + 3 x² = 76
5 x² - 20 x - 60 = 0
We apply the solving formula for second order equations and we get x₁ = 6 and x₂ = -2.
If we replace these x values in [1], we get:
y₁ = 4 - x₁ = 4 - 6 = -2
y₂ = 4 - x₂ = 4 - (-2) = 6
As a consequence, one of the numbers is 6 and the other is -2.
relationship between team performance and team dynamics
Answers
Answer:
Group dynamics can be understood as how team member's distinct roles and behaviours impact other group members and the group as a whole. Team dynamics are therefore the unconscious, psychological factors that influence the direction of a team's behaviour and performance.
error in library( ) : there is no package called ‘ ’
Answers
Answer:
To run R scripts using Rscript and loading necessary packages, you need to ensure that the package paths are correctly set up. The following steps could help resolve the issue:
Check if the package is installed using .libPaths() and installed.packages() commands in R, and ensure the package is available.
Run Sys.getenv('R_LIBS_USER') in R console to get the user library directory for the R environment in use.
Run Rscript.exe -e "Sys.getenv('R_LIBS_USER')" on the command line to get the user library directory for the Rscript environment.
Ensure you set the same R_LIBS_USER environment variable in R and Rscript using Sys.setenv("R_LIBS_USER"="path/to/user/library") in R.
Run Rscript.exe -e ".libPaths()" on the command line, and ensure the value returned is the same as the R_LIBS_USER path set in step 4.
Note: Remember that paths to libraries contain either backslashes () or forward slashes (/), depending on the operating system being used.
Example code:
library(timeSeries) #This is the package that failed to load
To fix the issue:
# From the R console
.libPaths() # Get the user library path
# From the command line
Rscript.exe -e "Sys.getenv('R_LIBS_USER')" # Get the user library path for Rscript
# Set R_LIBS_USER environment variable in R
Sys.setenv("R_LIBS_USER"="path/to/user/library") # Replace path/to/user/library with the actual directory to user/library
# Set R_LIBS_USER environment variable in Rscript
setenv R_LIBS_USER=path/to/user/library # Replace path/to/user/library with the actual directory to user/library
# Compare paths from R and Rscript
Rscript.exe -e ".libPaths()" # Compare with R_LIBS_USER path
library(timeSeries) # Should work now!
Regarding the installation issue of packages, it may be a permission issue and running the R session as administrator may help. Additionally, make sure that the directory where packages are installed has write permissions for the current user.
Example code:
install.packages("ggplot2") # Ensure double quotes are used with package name
To fix the issue:
Try running R or RStudio as administrator.
Check the
Explanation:
Fill in the tables and find the equivalent resistance for the following circuits:
Answers
Answer:
12 32
Explanation:
Which of the following wouldn't be pictured on a fan motor's ladder logic diagram? A. Auxiliary contacts B. two Push-button control C. Boiler D. Mixing chamber
Answers
Answer:
c
Explanation:
:)
If an oncoming driver crosses into your path of travel, the space that is usually available for you to move your vehicle is.
Answers
Answer:
If an oncoming driver crosses into your path of travel, the space that is usually available for you to move your vehicle is to the right of your vehicle.
Explanation:
On many roads, there are areas on the sides of the road called the shoulder. The shoulder can be used for pulling over and stopping your vehicle due to emergencies.
If a driver crosses into your lane coming straight for you, the best thing to do is to pull over to the shoulder as fast as possible so to not turn left and hit incoming traffic.
6.03 Discussion: Then & Now - Safety
Discussion Topic
I'm Done
In this unit, you have learned about the evolution of the industry’s machines, through both technology and innovation. These improvements have reduced risk and injury to the Operating Engineers.
Choose one innovation or device.
Explain why you think that technology is the most important advancement in Operating Engineers’ safety.
Answers
Answer:
Information technology is important in our lives because it helps to deal with every day's dynamic things. Technology offers various tools to boost development and to exchange information. Both these things are the objective of IT to make tasks easier and to solve many problems.
where is the buttock line or buttline of an aircraft
Answers
The buttock line, also known as the buttline, of an aircraft refers to an imaginary line that runs along the longitudinal centerline of the fuselage.
The buttock line is an important reference line used in aircraft design and analysis. It represents the symmetry axis of the aircraft and is often used as a baseline for various measurements and calculations. It serves as a common reference point for determining the position of components, such as the wings, empennage, and engines, in relation to the centerline of the aircraft. The buttock line helps ensure that these components are properly aligned and balanced for optimal aerodynamic performance and stability.
In addition to its use in design and analysis, the buttock line is also relevant in aircraft maintenance and inspection. It aids in locating and identifying structural features and access points along the fuselage, facilitating maintenance activities and ensuring compliance with safety regulations.
Overall, the buttock line is a significant reference line in aircraft design, serving as a baseline for various measurements, calculations, and component positioning. It helps ensure proper alignment, balance, and functionality of the aircraft's components, contributing to its overall performance and safety.
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The steel shaft has a diameter of 40 mm and is fixed at its ends A and B . If it is subjected to the couple determine the maximum shear stress in regions AC and CB of the shaft. G st = 75 GPa.
Q6/
Answers
Answer:
See explanation.
Explanation:
Since no figure was given I solved a problem that was similar to the one you described that I worked in my mechanics of materials class. The method should be very similar for your figure. See attached image for my work.
If it is subjected to the couple determine the maximum shear stress in regions AC and CB of the shaft. G st = 75 GPa. Than the answer will be 52Mpa.
What we need to perform?We need to perform a two step process to obtain the maximum shear stress on the shaft. For the solid shaft,
P=2×pi×N×T/60 or T=60×p/2×pi×N
Where P=power transmitted by the shaft=50×10³W
N=rotation speed of the shaft in rpm=730rpm
Pi=3.142
T is the twisting moment
By substituting the values for pi, N and P, we get
T=654Nm or 654×10³Nmm
Also, T=pi×rho×d³/16 or rho=16×T/pi×d³
Where rho=maximum shear stress
T = twisting moment=654×10³Nmm
d= diameter of shaft= 40mm
By substituting T, pi and d
Rho=52Mpa
b. For a hollow shaft, the value for rho is unknown
T=pi×rho(do⁴-di⁴/do)/16
Rho=T×16×do/pi×(do⁴-di⁴)
Where
T= twisting moment=654×10³Nmm gotten above
do=outside shaft diawter=40mm
di= inside shaft diameter =30mm
Pi=3.142
Substituting values for pi, do, di and T.
Rho=76Mpa
Therefore, If it is subjected to the couple determine the maximum shear stress in regions AC and CB of the shaft. G st = 75 GPa. Than the answer will be 52Mpa.
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who is the strongest avenger i say hulk but who knows at this point
Answers
Answer:
or is the strongest evenger she hulk
Explanation:
?????????
Answer:
Thor!
Explanation:
In Thor: Ragnarok he beat the Hulk in order for Hulk to win thor had to be electrocuted and in Avengers: Endgame Thor is seen holding open the "Floodgates" and withstanding the radiation from a dying star, also the fact that Thor is a god means that he is all powerful and the rightful heir to the throne to Asgard, plus the fact that he has defeated Loki multiple times a feat that not even the Hulk has done.
Which ratio shows the relationship between the sizes of the model and the actual car
Answers
Answer:
The scale factor is used to make models of real-life objects. For example, a toy car is modeled to look just like a real car but at a smaller size. The ratio of the toy car to the real car might be 1:24 1: 24 . Which means that for every one unit of length on the toy car, the real thing is 24 times that size.
Explanation:
Define a separate subroutine for each of the following tasks respectively.
A) Swap the most significant bit (msb) of registered AH And the Least significant Bit (Lsb) of registered AL.
B) Check the msb of AL and LSB of BL. if they are equal, copy BL into AL. Otherwise copy AL in BL
C) set all the bits in LS Nibble and Invert All bits in the MS nibble of the word at offset address 0400H in the data segment.
D) multiply the byte at offset address 0100h with the byte at offset address 0200h. save the result at offset address 0300h in the data segment.
pls answer i took hours to write these
Answers
Answer:
I HAVE NO CLUEEEE
Explanation:
???????????????????/
Answer:
I think its B
Explanation:
Im sorry if im wrong
Under normal operating conditions, the electric motor exerts a torque of 2.8 kN-m.on shaft AB. Knowing that each shaft is solid, determine the maximum shearing stress in a) shaft AB b) shaft BC c) shaft CD (25 points) Given that the torque at B
Answers
Answer:
Explanation:
The image attached to the question is shown in the first diagram below.
From the diagram given ; we can deduce a free body diagram which will aid us in solving the question.
IF we take a look at the second diagram attached below ; we will have a clear understanding of what the free body diagram of the system looks like :
From the diagram; we can determine the length of BC by using pyhtagoras theorem;
SO;
\(L_{BC}^2 = L_{AB}^2 + L_{AC}^2\)
\(L_{BC}^2 = (3.5+2.5)^2+ 4^2\)
\(L_{BC}= \sqrt{(6)^2+ 4^2}\)
\(L_{BC}= \sqrt{36+ 16}\)
\(L_{BC}= \sqrt{52}\)
\(L_{BC}= 7.2111 \ m\)
The cross -sectional of the cable is calculated by the formula :
\(A = \dfrac{\pi}{4}d^2\)
where d = 4mm
\(A = \dfrac{\pi}{4}(4 \ mm * \dfrac{1 \ m}{1000 \ mm})^2\)
A = 1.26 × 10⁻⁵ m²
However, looking at the maximum deflection in length \(\delta\) ; we can calculate for the force \(F_{BC\) by using the formula:
\(\delta = \dfrac{F_{BC}L_{BC}}{AE}\)
\(F_{BC} = \dfrac{ AE \ \delta}{L_{BC}}\)
where ;
E = modulus elasticity
\(L_{BC}\) = length of the cable
Replacing 1.26 × 10⁻⁵ m² for A; 200 × 10⁹ Pa for E ; 7.2111 m for \(L_{BC}\) and 0.006 m for \(\delta\) ; we have:
\(F_{BC} = \dfrac{1.26*10^{-5}*200*10^9*0.006}{7.2111}\)
\(F_{BC} = 2096.76 \ N \\ \\ F_{BC} = 2.09676 \ kN\) ---- (1)
Similarly; we can determine the force \(F_{BC}\) using the allowable maximum stress; we have the following relation,
\(\sigma = \dfrac{F_{BC}}{A}\)
\({F_{BC}}= {A}*\sigma\)
where;
\(\sigma =\) maximum allowable stress
Replacing 190 × 10⁶ Pa for \(\sigma\) ; we have :
\({F_{BC}}= 1.26*10^{-5} * 190*10^{6} \\ \\ {F_{BC}}=2394 \ N \\ \\ {F_{BC}}= 2.394 \ kN\) ------ (2)
Comparing (1) and (2)
The magnitude of the force \(F_{BC} = 2.09676 \ kN\) since the elongation of the cable should not exceed 6mm
Finally applying the moment equilibrium condition about point A
\(\sum M_A = 0\)
\(3.5 P - (6) ( \dfrac{4}{7.2111}F_{BC}) = 0\)
\(3.5 P - 3.328 F_{BC} = 0\)
\(3.5 P = 3.328 F_{BC}\)
\(3.5 P = 3.328 *2.09676 \ kN\)
\(P =\dfrac{ 3.328 *2.09676 \ kN}{3.5 }\)
P = 1.9937 kN
Hence; the maximum load P that can be applied is 1.9937 kN
Analyse how BIM can support the delivery of construction projects in a more sustainable manner.
Answers
Building Information Modelling (BIM) can support the delivery of construction projects in a more sustainable manner by enabling designers, engineers and builders to collaborate more effectively and make more informed decisions throughout the project lifecycle.
By creating a digital model of the building, BIM can help to identify and address potential sustainability issues, such as energy consumption and waste reduction, at an early stage. BIM also enables the integration of sustainable materials and technologies, which can help to reduce the environmental impact of the building. Additionally, BIM can support the efficient use of resources, such as water and energy, by providing accurate information about the building's performance. In conclusion, BIM can play a vital role in the delivery of construction projects in a more sustainable and environmentally responsible manner.
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A storage tank is purged continuously with a stream of nitrogen. The purgestream leaving the tank is saturated with the product stored in the tank. A majorpart of the product lost in the purge could be recovered by installing a scrubbingtower to absorb the product in a solvent. The solution from the tower could befed to a stage in the production process, and the product and solvent recoveredwithout significant additional cost. A preliminary design of the purge recoverysystem has been made. It would consist of:1. A small tower 0.5 m diameter, 4 m high, packed with 25 mm ceramic saddles,packed height 3 m.2. A small storage tank for the solution, 5 m3 capacity.3. The necessary pipe work, pump, and instrumentation.All materials of construction, carbon steel.Using the following data, evaluate whether it would be economical to install therecovery system:1. cost of product £5 per kg,2. cost of solvent 20 p/kg,3. additional solvent make-up 10 kg/d,4. current loss of product 0.7 kg/h,5. anticipated recovery of product 80 per cent,6. additional service(utility) costs, negligible.Other operating costs will be insignificant.
Answers
Answer:
It is economical
Explanation:
Given data for determining
cost of product = £5 per kg
cost of solvent = £20 per /kg
additional solvent makeup = 10 kg/d
current loss of product = 0.7 kg/h
anticipated recovery of product = 80%
additional service ( utility cost ) = negligible
Determine if it is economical to install the recovery system
cost of product = £5 per kg
cost of solvent = £20 per /kg
additional solvent required = 10 kg / d
cost of additional solvent in a day = £200 / day ( £20 per kg * 10 kg / d )
product lost = 0.7 kg/h
product recovered = 0.7 * 80% = 0.56 kg/h
therefore product recovered in a day = 0.56 * 24 = 13.44 kg / day
Next :
calculate income generated from product recovery
13.44 kg/day * £20 /kg = £268.88 / day
Determine if it is economical
Income - cost
= £268.88 - £200
= £68.88 ( hence it is economical )
1. Describe an occasion in which an explanatory sketch would be used.
the end user how
Answers
Answer:
building a bridge
Explanation:
you would have to sketch ideas to see what the bridge would look like and you need to know what to add to it to enhance the percentage of it working. if you sketch it you would have an idea of the process also
Building a bridge is an occasion in which an explanatory sketch would be used.
What is meant by explanatory sketch ?Sketches of explanations are created to demonstrate form, structure, and function. They accurately and objectively communicate a design, placing more emphasis on explanation than pitch. Outside of the design team, explanation sketches must be understandable.
Exploratory sketches, often referred to as thinking drawings, are a type of personal communication that frequently serve as the starting point for brand-new product concepts.
During a brainstorming session or for personal usage in a design notebook, these quick sketches are meant to quickly capture ideas. Exploratory research aims to study the important aspects of a topic that hasn't gotten much attention.
Thus, it is Building a bridge.
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raw sugar cane is taken into a process to create sugar, which is essentially sucrose. the raw cane is approximately 16% sucrose, 63% water, and the rest fiber by mass. juice from the cane is extracted by passing the cane through a series of crushers. about 5% extra mass of water is added to the sugar cane prior to this step to help in the extraction process. the crushed cane and liquid juice is sent to a filter press that creates a cake that contains 4% of the weight of the cane juice, which has a composition similar to the overall non-fiber content of the raw cane. the filtrate is sent to an evaporator where enough water is evaporated to obtain a pale yellow juice that is 41% water. a
Answers
The juice is then sent to a crystallizer where it is cooled and seeded with sugar crystals. The crystals grow in size and are separated from the liquid by centrifugation.
What is a crystallizer?Crystallizer is a type of signal-processing technology most commonly used in audio production. It is designed to add clarity and definition to audio signals by emphasizing the frequencies which are most important to the signal. It works by amplifying the signal in the frequency domain and adding a process of resonance so that certain frequencies are emphasized, giving a more defined sound. Crystallizer is particularly useful in mastering, where it can bring out details and clarity that would otherwise be lost. It can also be used to enhance percussion instruments, making them more present in a mix.
The crystals are then dried and screened to obtain the desired size of sugar crystals. The remaining liquid is sent to a vacuum pan where it is boiled and evaporated until it reaches a concentration of 65% sucrose. The syrup is then cooled and crystallized to obtain the final product, which is refined sugar.
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Type the correct answer in the box. Spell all words correctly.
Convert calories to joules.
3 calories is ____ joules
Answers
Answer:
46
Explanation:
Answer:
12.55 Joules
Explanation:
For edmentum users :)
If a circuit produces a phase shift of 45 degrees between the voltage and current curves and the apparent power is 100 VA, what is the TRUE power in the circuit?
50 W
70.7 VA
70.7 W
100 A
Answers
The true power is obtained as 70.7 VA.
What is the true power?We define the power a the rate of doing work, we know that the power in a circuit is the product of the current and the voltage. In this case, we want to find the true power thus we have to involve the use of the phase shift in degrees.
Thus;
True power = PcosΦ
P = 100 VA
Φ = 45 degrees
True power = 100 VA * cos 45 degrees
True power = 70.7 VA
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A "calorie" is a unit of energy, defined as the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. The nutritional labels on food products typically tell you how many calories of digestible energy are in one serving of food, where "digestible" means that the energy stored in the chemical bonds of the molecules comprising the food can be extracted by your body. (Water for example has energy, but that energy is not chemically accessible via digestion.) To simplify understanding for typical consumers, the "calories" reported on nutritional labels actually represent kilocalories: a 170 calorie can of beer actually contains 170,000 calories of digestible energy.
i) If a student foolishly decides to binge drink 21 beers on their 21t birthday, how many gallons of water could they have heated from room temperature (24 °C) to boiling (100 C) using an equivalent amount of digestible energy in the beer? Recall that one gallon of water is roughly 8 pounds.
ii) What is this energy equivalent to in BTU? A "BTU" or British Thermal Unit is also a unit of energy, defined as the amount of energy needed to raise the temperature of one pound of water by one degree Fahrenheit
iii) If you had purchased an equivalent amount of electrical energy in kW-hr from the utility company, how much would you have to pay? Is this cheaper than buying beer?
Answers
A "calorie" is a unit of energy that is defined as the usually inform you of the number of calories of digestible energy present in one serving of food. 21 beers times 17 calories per beer equals 357 calories.
What is "calorie"?Calories are units of energy that a food or drink provides. You can usually find calorie counts listed on food items, and wearables like the best fitness trackers allow you monitor how many calories you're burning by doing different activities. Certain foods, such as fatty, fried, or processed foods, tend to have more calories. Other foods, such as fresh fruit and vegetables, tend to have fewer calories. However, some healthy fruits and vegetables can be high in calories, while low-calorie foods, such as diet soda, don’t provide any nutritional value. We need calories to give us enough energy to move around, stay warm, grow, work, think, and play. Even our blood circulation and digestion need the energy gained from calories in order to function well.To learn more about blood circulation refer to:
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Identify three advantages to being accountable for your gear in the fire camp
Answers
Being accountable for your gear in the fire camp is essential, and it is important to ensure that you have all of the necessary equipment for the job. There are several advantages to being accountable for your gear in the fire camp, and Increased efficiency:
One of the biggest advantages of being accountable for your gear in the fire camp is increased efficiency. When you have all of the necessary equipment and know exactly where it is, you can quickly and easily access it when you need it. This can help you to work faster and more efficiently, which can be critical in a fire situation
Safety: Another advantage of being accountable for your gear in the fire camp is safety. When you have all of your equipment and know exactly where it is, you can ensure that you are properly protected at all times. This can be especially important in a fire situation where there are many hazards present.
Better communication: being accountable for your gear in the fire camp can lead to better communication. When everyone knows where their gear is and has it readily available, they can communicate more effectively with one another. This can help to ensure that everyone is on the same page and that there are no misunderstandings or miscommunications.
Being accountable for your gear in the fire camp is critical for a successful mission. By keeping track of your equipment and ensuring that it is always available when you need it, you can increase efficiency, safety, and communication, which can be essential in a fire situation.
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All of the following are types of stripping except? a.end terminations b. window cuts c. spiral cuts d. indent cuts
Answers
The option that is not a types of stripping is option d. indent cuts.
What are the types of cable stripping?
They are:
1. End termination
2. window cut
3. cut spiral cut
4.circumferential and longitudinal cuts
Wire Stripping is known to be a kind of act where there is the removing of the material information from any kind of cable or wire transfers, thus making it hard to identify.
Therefore, The option that is not a types of stripping is option d. indent cuts.
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Determine the volume of a 6-foot cube.
Answers
The rate of change of the radius with time is a partial derivative of the rate of change of volume with time. At the instant the height of the cylinder is 6 feet is the radius is decreasing at a rate of approximately 4.634 ft./s.
What is the height of the cone?The height of the cone is 27 meters when the radius of the cone is 55 meters and the volume of the cone is 733 cubic meters.The radius of a cylinder is increasing at a constant rate of 3 meters per second, and the volume is increasing at a rate of 108 cubic meters per second.
Cones grow in size at constant rates of 9 meters per second for the radius and 1631 cubic meters per second for the volume.
Therefore, The height of the cone is 27 meters when the radius of the cone is 55 meters and the volume of the cone is 733 cubic meters.
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what is the dimensions of beta
Answers
Answer:
byee byee bbbbbbbbbbbb
in the 2010 toyota prius, a boost converter is used to step up the output voltage of the battery (assumed to have constant voltage of 200 v) to the dc-bus voltage level of 250 v. assuming the converter to be ideal, what is the duty cycles needed to do this at steady-state?
Answers
Boost converters can also supply power to smaller-scale equipment, including portable lighting systems.
A boost converter can increase the voltage from a single 1.5 V alkaline cell to provide the lamp with the 3.3 V that a white LED generally needs to emit light. High-frequency power conversion circuits known as DC-DC converters use inductors, transformers, and capacitors to reduce switching noise and produce regulated DC voltages. Even with fluctuating input voltages and output currents, closed feedback loops maintain constant voltage output. To "step-up" an input voltage to a higher level, needed by a load, the boost converter is utilized. By holding energy in an inductor and delivering it to the load at a greater voltage, this special feature is made possible.
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The most common type of pressure gauge is the 1. Piston 2. Linkage 3. Bourdon Tube 4. 5. Temperature
Answers
Answer:
Bourdon Tube gauge
Explanation:
The most popular type of pressure gauge in several countries is the Bourdon pressure tube gauge, that is used to determine medium and high loads. Bourdon tube will measure pressures ranging between 600 mbar - 4,000 bar. While the inner pressure is greater than the exterior pressure, the tube pushes forward, and vise versa.
An effectively delivered lesson brings closure to students. Which of the following are benefits of providing closure in a lesson for middle grade students? Select all that apply.
Confirm understanding of what was learned.
Self-assess understanding of what was taught.
Share learning with peers.
Reinforce the concepts which were taught.
Reflect on how they engaged with the learning
Answers
Of the following, the ones that are benefits of providing closure in a lesson for middle-grade students are:
Confirm understanding of what was learned. (Option A)Self-assess understanding of what was taught. (Option B)Share learning with peers. (Option C)Reinforce the concepts which were taught. (Option D)Reflect on how they engaged with the learning. (Option E)What is closure in education?Closure refers to what the teacher performs at the conclusion of the class to promote wrap-up - it is a fast review to remind students what they have learned (or should have learned) and allows you to assess where the students are to aid you in planning the next lesson.
Closure as a teaching approach refers to the teacher's attempts to assist students in seeing the logical order of the lesson at key intervals during the presentation of subject/course materials and learning activities. What has a beginning should have a conclusion. What starts well should end well.
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estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.29 mm and that has a tip radius of curvature of 0.004 mm when a stress of 1300 mpa is applied.
Answers
The theoretical fracture strength of the brittle material is estimated to be approximately 165.6 MPa when a stress of 1300 MPa is applied and fracture occurs by the propagation of an elliptically shaped surface crack of length 0.29 mm and tip radius of curvature of 0.004 mm.
To estimate the theoretical fracture strength of a brittle material given the information provided, we can use Griffith's theory of brittle fracture. According to this theory, the fracture strength of a brittle material can be expressed as:
σ_f = (2Eγπa)^0.5
where σ_f is the fracture strength, E is the elastic modulus, γ is the surface energy per unit area, and a is the length of the elliptically shaped surface crack.
To calculate the fracture strength, we need to first determine the surface energy per unit area of the material. For glass, a typical value of surface energy is around 1 J/m^2.
Given the length of the elliptically shaped surface crack (a) is 0.29 mm, and the tip radius of curvature is 0.004 mm, we can calculate the crack area (A) as follows:
A = πab = π(0.29/2)(0.004)
A ≈ 5.67 x 10^-7 m^2
Next, we can calculate the elastic modulus (E) of the material. For glass, the elastic modulus is typically around 70 GPa.
Substituting these values into the equation for fracture strength, we get:
σ_f = (2Eγπa)^0.5 = [2(70 x 10^9)(1)(π)(0.29 x 10^-3)]^0.5
σ_f ≈ 165.6 MPa
Learn more about theoretical fracture strength at: https://brainly.com/question/13707729
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