The total running time for inserting N elements in a min-heap with N elements, in the worst-case scenario, is O(N). Therefore, the correct answer is option (c) O(N) worst case.
In this question, we are given a min-heap with N elements, and we need to determine the total running time for inserting N elements in the worst-case scenario. Min-heaps are binary trees that maintain a specific order, with the smallest element being the root node. When inserting an element in a min-heap, the process usually takes O(logN) time due to the height of the binary tree. However, when inserting N elements, the running time is calculated by the sum of the heights of the binary tree at each insertion.
The sum of the heights of a complete binary tree at each insertion can be represented as:
O(log1) + O(log2) + O(log3) + ... + O(logN)
This series is an example of a harmonic series and can be approximately evaluated as O(NlogN). However, we can further optimize the insertion process by building the min-heap using a bottom-up approach. This approach allows us to construct the min-heap in O(N) time, which is faster than the O(NlogN) approach.
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A brine solution is 26% salt with 70.0 kg of water evaporated per hour. To produce 195 kg of pure salt (0% moisture) per day, how long should the process operate each day and how much brine must be fed to the evaporator per hour?
The process should operate each day for ___ hours.
The amount of brine that must be fed to the evaporator is ___ kg/h.
Answer:
- the process should operate each day for 7.9286 hours
- the amount of brine that must be fed to the evaporator is 94.594 kg/hr
Explanation:
Given that;
concentration of brine = 26%
so water concentration will be 100% - 26% = 74%
for evaporation of 70kg water per hour, residual is pure salt( 0% moisture)
so mass flow rate of brine = 70/(74%) = 70/0.74 = 94.5945 kg/hr
Amount of pure dry salt produced(0%) = 94.5945 - 70 = 24.5945 kg/hr
Now for production of 195kg of pure dry salt, number of hours required will be
T = 195 / 24.5945 = 7.9286 hrs
Therefore the process should operate each day for 7.9286 hours.
Total brine solution required ( 26% salt conc.) = 195/0.26 = 750 kg
Feed rate of brine solution ( 26% salt conc.) = 750 / 7.9286 = 94.594 kg/hr
Therefore the amount of brine that must be fed to the evaporator is 94.594 kg/hr
In a series motor, the field electromagnet consists of A) a winding connected in parallel with the armature. B) a winding connected in parallel with the armature and a second winding connected in series with the armature. C) a winding connected in series with the armature. D) a winding connected in series with a separate dc power source.
Answer:
C) a winding connected in series with the armature.
Explanation:
In a series motor, an electromagnet is used as a stator to generate its magnetic field. The field coil of this stator are connected through a commutator in series with the rotor windings. This stator which is the armature windings will conduct AC even on a DC machine, due to the periodically reverses current direction (commutation) or due to electronic commutation (as in brushless DC motors).
how many rotations of the crankshaft are required to complete each stroke of a four-stroke cycle engine?
Escribe dos gemplos de los cambios de conducta que
adquiere el trabajador
al momento de capacitarse.
Aprendizajes del buen vivir ya que al compartir con la comunidad y te desarrollas, tu desarrollas otra manera de pensar y adquieres el aprendizaje del buen vivir con todos sin excepción alguna
Además el aprendizaje de experimentar compartir con otras personas que no son tu familia, eso hará que desarrolles el aprendizaje de tus cualidades y en este caso sería la cualidad de la imparcialidad
Which of the following Belt Levels usually require a Six Sigma Project be completed before a Six Sigma Certification is awarded?
A . White Belt
B . Yellow Belt
C . Green Belt
D . Black Belt
E . Master Black Belt
F . None of the Above
G . All of the above
It is to be noted that "All of the above" (Option G) Belt Levels must be completed before a Six Sigma Certification is awarded.
What is a Six Sigma Certification?Six Sigma is a certification program that teaches employees how to analyze processes and results in the objective of eliminating waste and faults. There are numerous levels of certification, ranging from main end user to master Six Sigma user.
Six Sigma is a quality control certification that teaches employees how to analyze processes and outcomes in order to eliminate waste and faults. Certification levels range from primary end user to master Six Sigma user who serves as a senior quality control member.
It is to be noted that the ASQ Six Sigma Black Belt exam is a demanding and tough exam. The disciplined study, experience, and a solid preparation and test-taking plan are required. Many students study for months and then fail.
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If there is a discrepancy between Chick-fil-A food safety requirements and local Health Department
regulations, what should Team Member do?
The following should be done by the team member:
It is important to follow both Chick-fil-A food safety requirements and local Health Department regulations. In the case when there is a discrepancy between the two, always follow the more stringent requirement. Any other appearance or grooming issue not covered in these materials may be addressed at the discretion of the Operator.
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What is the Laplace Transform of:
f(t)=6e^(−5t)+e^(3t)+5t^3−9
\(\boxed{ℒ_t[f(t)] =\frac{30}{{s}^{4} } - \frac{9}{s} + \frac{6}{s + 5} + \frac{1}{s - 3}} \)
This holds true because:
\(\lim_{s\to\infty} [\frac{30}{{s}^{4} } - \frac{9}{s} + \frac{6}{s + 5} + \frac{1}{s - 3}] =0 \)
[The answer is throughly verified, hence you can trust this :)]
1 Define the following technical terms: A) Sewage Factor B) Connection Factor C) Infiltration Coe. D) Design Period E) Drop Manhole F) Self Cleansing velocity 2 Which factors do affect on water demand
A) Sewage Factor: It represents the proportion of water inflow that is expected to be discharged as sewage. It is used in the design of sewer systems to estimate the quantity of sewage flow that will be generated.
B) Connection Factor: It represents the percentage of buildings or properties that are expected to connect to a sewer system. It is used in the design of sewer systems to estimate the total number of connections that will be made to the system.
C) Infiltration Coefficient: It represents the rate at which water enters a sewer system through cracks, joints, and other defects in pipes. It is used in the design of sewer systems to estimate the volume of infiltration that will occur during wet weather conditions.
D) Design Period: It is the length of time for which a particular engineering project is designed to function effectively. For example, in the case of water supply systems, the design period may be 20-30 years, during which the system is expected to meet the water demand requirements of the users.
E) Drop Manhole: It is a type of manhole that is constructed at a location where the sewer pipe changes direction from a horizontal to a vertical alignment. The purpose of a drop manhole is to reduce the velocity of the sewage flow and prevent damage to the downstream sewer structures.
F) Self Cleansing Velocity: It is the minimum velocity required in a sewer pipe to prevent the deposition of solids and ensure the self-cleansing of the pipe. A value of twice the average velocity is commonly used as the self-cleansing velocity.
The factors that affect water demand include population size, economic activity, climate, lifestyle, and water pricing policies. Changes in any of these factors can influence the level of water demand in a given area. For example, an increase in population size or economic activity can lead to a higher demand for water, while the implementation of water conservation measures can reduce water demand.
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The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with mean μ=1497 and standard deviation σ=322. A certain test-retake preparation course is designed for students whose SAT scores are in the lower 25%, percent of those who take the test in a given year. What is the maximum SAT score in 2014 that meets the course requirements?
Answer:
1279
Explanation:
We have the mean u = 1497
Standard deviation sd = 322
We find the x distribution using 25%
P(Z<z) = 0.25
Z = -0.675
From here we use the formula for z score
X = z(sd) + u
X = -0.675*322 + 1497
X = -217.35 + 1497
X = 1279.6
Which is approximately 1279
So we conclude that the maximum sat scores in year 2014that meets with the requirements of this course is 1279
Answer:
1831
Explanation:
When pulling a trailer down a long steep hill, you should not do which of the following?A. drive in a lower gearB. increase speedC. keep in the right laneD. maintain a space cushion between vehicles
When pulling a trailer down a long steep hill, it is important to take certain precautions to ensure your safety and the safety of other drivers on the road. One of the most important things to remember is to never increase your speed.
Instead, it is recommended that you drive in a lower gear, which will help to control your speed and reduce the risk of losing control of your trailer. By driving in a lower gear, you can also use your vehicle's engine to slow down, rather than relying solely on your brakes. This is important because overheating your brakes can cause them to fail, which can be dangerous when you are towing a heavy load.
In addition to driving in a lower gear and avoiding speeding, it is also important to maintain a safe following distance between your vehicle and other vehicles on the road. This will help to ensure that you have enough time to react if the vehicle in front of you suddenly stops or slows down. It is also a good idea to keep to the right lane when going down a steep hill, as this can help to reduce the risk of collisions with other vehicles.
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Who should inspect a crane?
1Employer
2Experience workers
3Foreman
4Competent person
Answer:
4. Competent person
Explanation:
A competent person should inspect the crane
OSHA regulations only require that such equipment be inspected during initial use and annually thereafter by a "competent person"
A company recently experienced an attack during which its main website was directed to the attacker's web server, allowing the attacker to harvest credentials from unsuspecting customers. Which of the following should the company implement to prevent this type of attack from occurring in the future?
IPSec
SSL/TLS
DNSSEC
S/MIME
The company should implement SSL/TLS to prevent this type of attack from occurring in the future.
SSL/TLS (Secure Sockets Layer/Transport Layer Security) is a protocol used to provide secure communication over the internet. It ensures the confidentiality and integrity of the data being transmitted between two systems, such as a web server and a client's web browser.
In this case, SSL/TLS can prevent the attack by ensuring that the communication between the company's web server and a client's web browser is encrypted and authenticated. With SSL/TLS, the attacker cannot redirect the client's web browser to their own server without being detected, as the encryption ensures that the client's browser can only communicate with the legitimate web server.
IPSec (Internet Protocol Security) is another protocol that provides secure communication over the internet. However, it is more commonly used for site-to-site VPN (Virtual Private Network) connections rather than web traffic.
DNSSEC (Domain Name System Security Extensions) is a protocol that adds security to the domain name system (DNS) by digitally signing DNS records. It does not prevent attacks on the company's website.
S/MIME (Secure/Multipurpose Internet Mail Extensions) is a protocol used for securing email communication. It is not relevant to the company's website and does not prevent attacks on it. Thus, SSL/TLS is the right answer.
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Discuss the relation between the force exerted and pressure.
Answer:
When a force is exerted on an object it can change the object's speed, direction of movement or shape. Pressure is a measure of how much force is acting upon an area. Pressure can be found using the equation pressure = force / area. Therefore, a force acting over a smaller area will create more pressure
Explanation:
hope it will become helpful to you ☺️☺️
Gold forms a substitutional solid solution with silver. Calculate the number of gold atoms per cubic centimeter (in atoms/cm3) for a silver-gold alloy that contains 19.0 wt% Au and 81.0 wt% Ag. The densities of pure gold and silver are 19.32 and 10.49 g/cm3, respectively, and their respective atomic weights are 196.97 and 107.87 g/mol.
The number of gold atoms per cubic centimeter in the silver-gold alloy is 1.44 x 10^22 atoms/cm3.
Determine the alloy's density. Determine the molar composition of the alloy . Determine the number of atoms of gold per cubic centimetre. Find out the alloy's molar composition. We must convert the mass fractions of gold and silver to molar fractions in order to estimate the alloy's molar composition. Silver's molar fraction is equal to 0.930 by multiplying (0.810 x (196.97 g/mol + 107.87 g/mol)) by (107.87 g/mol x 12.05 g/cm3). Determine the amount of atoms of gold per cubic centimetre . Ultimately, we can determine how many gold atoms there are in every cubic centimetre. As a result, the silver-gold alloy has 1.44 x 1022 gold atoms per cubic centimetre.
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Consider the flow of mercury (a liquid metal) in a tube. How will the hydrodynamic and thermal entry lengths compare if the flow is laminar
Answer:
Explanation:
Considering the flow of mercury in a tube:
When it comes to laminar flow of mercury, the thermal entry length is quite smaller than the hydrodynamic entry length.
Also, the hydrodynamic and thermal entry lengths which is given as DLhRe05.0= for the case of laminar flow. It should be noted however, that Pr << 1 for liquid metals, and thus making the thermal entry length is smaller than the hydrodynamic entry length in laminar flow, like I'd stated in the previous paragraph
cache memory is available in two forms: level 1, which is found on the cpu chip, and level 2, which can be accessed over a high-speed dedicated interface.
This statement is generally true.Cache memory is a type of high-speed memory that is used to improve the performance of a computer by reducing the time it takes to access data from main memory.
Cache memory is typically available in two or more levels, with each level providing a progressively larger and slower cache.Level 1 (L1) cache is the smallest and fastest cache, and it is typically located directly on the CPU chip. This allows for extremely fast access to frequently used data and instructions, which can significantly improve performance.Level 2 (L2) cache is typically larger than L1 cache and is located on a separate chip that is connected to the CPU through a high-speed dedicated interface, such as a backside bus. This allows for faster access to frequently used data than main memory, but it is slower than L1 cache.
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In an orthogonal cutting, a cylinder is turned to reduce the diameter with the following processing conditions Initial diameter Depth of cut Feed Rake angle Chip-tool contact length Cutting force Thrust force Spindle RPM 100 mm 2 mm 0.1 mm/rev 10° 0.5 mm 450 N 150 N 60 Calculate a) Shear and normal stresses on chip-tool interface b) Shear angle using the Lee and Shaffer's model c) Chip thickness d) Shear and normal stresses on shear plane e) Specific cutting energy f) Spindle horse power
In an orthogonal cutting, a cylinder is turned to reduce the diameter with the following processing conditions Initial The spindle horse power is 11.78 kW.
Shear and normal stresses on the chip-tool interface To determine the shear stress (τ) and normal stress (σ) on the chip-tool interface, the following formula will be used:τ = the thrust force, t is the chip-tool contact length, is the width of the chip.t = 0.5 mm w = 0.1 mm/rev * 2 mm = 0.2 mmτ = 450 N / (0.5 mm * 0.2 mm) = 45000 N/m²σ = 150 N / (0.5 mm * 0.2 mm) = 15000 N/m²Therefore, the shear stress on the chip-tool interface is 45000 N/m², and the normal stress is 15000 N/m².
Shear angle using the Lee and Shaffer's model Lee and Shaffer's model can be used to calculate the shear angle (ϕ) using the formula:ϕ = (1 / tan α_r) * [(1 + sin ψ) / (cos ψ)]whereα_r is the rake angle andψ is the clearance angle.α_r = 10°ψ = 90° - 10° = 80°ϕ = (1 / tan 10°) * [(1 + sin 80°) / cos 80°] = 18.19°Therefore, the shear angle is 18.19°.
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Shear stress on chip-tool interface = 300 MPa ;Normal stress on chip-tool interface = 52.17 MPa ; Shear angle = 5.74°Chip thickness = 0.57 mm ; Shear stress on shear plane = 263.16 MPa ; Normal stress on shear plane = 45.79 MPa ; Specific cutting energy = 113398.2 N/m ; Spindle horse power = 8.44 hp.
Given data:
Initial diameter = 100 mm
Depth of cut = 2 mm
Feed = 0.1 mm/rev
Rake angle = 10°
Chip-tool contact length = 0.5 mm
Cutting force = 450 N
Thrust force = 150 N
Spindle RPM = 60
Formula used:
Shear force = Cutting force - Thrust force
Chisel angle = Tan-1(1/ Tan Φ - Tan Φ / Tan λ)
Shear angle = Tan-1(Tan Φ / (Cos λ - Sin Φ Sin λ))
Chip thickness = Feed / Sin λa)
Shear and normal stresses on chip-tool interface
Chip-tool contact length, l = 0.5 mm
Shear force, Fs = Cutting force - Thrust force= 450 - 150= 300 N
Area of contact, Ac = t × l= 2 × 0.5= 1 mm2
Shear stress, τ = Fs / Ac= 300 / 1= 300 MPa
Normal force, Fn = Fs Tan λ= 300 × Tan 10°= 52.17 N
Normal stress, σ = Fn / Ac= 52.17 / 1= 52.17 MPab)
Shear angle using the Lee and Shaffer's model
Here, λ = 10°
Chisel angle, Φ = Tan-1(1 / Tan λ)= Tan-1(1 / Tan 10°)= 5.71°
Shear angle, α = Tan-1(Tan Φ / (Cos λ - Sin Φ Sin λ))= Tan-1(Tan 5.71° / (Cos 10° - Sin 5.71° Sin 10°))= Tan-1(0.1)= 5.74°c) Chip thicknessHere, λ = 10°Feed, t = 0.1 mm
Chip thickness, h = t / Sin λ= 0.1 / Sin 10°= 0.57 mmd)
Shear and normal stresses on shear plane
Shear force, Fs = 300 N
Shear plane area, As = t × d= 2 × 0.57= 1.14 mm2
Shear stress, τ = Fs / As= 300 / 1.14= 263.16 MPa
Normal stress, σ = Fn / As= 52.17 / 1.14= 45.79 MPae)
Specific cutting energy
Cutting power, Pc = Fs × vc= Fs × πdn/1000= 300 × π × 100 × 60/1000= 5669.91 W
Specific cutting energy, E = Pc / Vt= Pc / (f × Vf)= 5669.91 / (0.1 × 0.5)= 113398.2 N/mmf)
Spindle horse power
Spindle power, Ps = Pc / η= Pc / 0.9= 5669.91 / 0.9= 6299.90 W= 6.2999 kW= 8.44 hp (1 hp = 0.7457 kW)
Therefore,
Shear stress on chip-tool interface = 300 MPa
Normal stress on chip-tool interface = 52.17 MPa
Shear angle = 5.74°Chip thickness = 0.57 mm
Shear stress on shear plane = 263.16 MPa
Normal stress on shear plane = 45.79 MPa
Specific cutting energy = 113398.2 N/m
Spindle horse power = 8.44 hp
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it's desired to preheat a light oil being fed to distillation column by running it through heat exchangers and the heating medium is the hot oil coming from the bottom of the column. conditions apply to each streamlight oil; flow rate 160m^3/hr, specific gravity 0.72,specific heat 1.76kj/kg k,specific temperature 300k , still bottom;120m^3/hr flow rate, specific gravity 0.74, specific heat 1.76kj/kg k, specific temperature 480k. light oil leaves heat exchanger at 360k, what temperature is the oil from the still bottom leaving the heat exchanger. determine maximum temperature attained by light oil in counter and co-current manner fluid flows
This question requires a thermal analysis of the heat exchanger system, which would involve the calculation of heat transfer rate and the resulting temperature change in both the light oil and the hot oil from the still bottom. This would require an understanding of heat transfer principles and the application of energy balance equations.
To determine the maximum temperature attained by the light oil in the heat exchanger, you would need to consider the flow arrangement of the two fluids, whether they are flowing in counter-current or co-current direction. This would affect the heat transfer rate and the resulting temperature change in each fluid.
To calculate the temperatures, you would need to consider the heat transfer rate between the two fluids, the inlet and outlet temperatures of each fluid, and their specific heat capacities. The equations would need to take into account the heat transfer rate, mass flow rate, and temperature change for each fluid.
Once the temperatures have been calculated, you can then determine the maximum temperature attained by the light oil and the hot oil, which would depend on the flow arrangement and the heat transfer rate between the two fluids.
It is recommended that you consult with a specialist in the field of thermal analysis or heat transfer to accurately and properly determine the maximum temperature attained by the light oil in the heat exchanger.
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Steven is starting a project that requires a specialized, experienced contractor. Which selection process is the most suitable for Steven's needs?
A. low-bid selection
B. qualification-based selection
C. best-value selection
D. private selection
Answer:
Option B, qualification-based selection
Explanation:
Whenever bidding is done for seeking professional services, selection of contractor should be done using qualifications-based selection.
While seeking professional service, focus is on selecting the best quality and value matter, hence the contracting agency with best experience and skill for the job is selected.
pls help me it’s due today
Answer:
C. 14.55
Explanation:
12 x 10 = 120
120 divded by 10 is 12
so now we do the left side
7 x 3 = 21 divded by 10 is 2
so now we have 14
and the remaning area is 0.55
so 14.55
When you hover over an edge or point, you are activating ____________ in SketchUp?
A. Zoom Focus
B. Inference Tools
C. Drawing Tools
D. Selection Filters
Which term is defined as an interrelated and harmonized collection of components and methods that transform inputs into​ outputs?
Consider an LRC series circuit. The impedance of the circuit increases if XC increases. When is this statement true?
Answer:
at frequencies below resonance
Explanation:
Below resonance, circuit impedance decreases as XC decreases with increasing frequency. Above resonance, circuit impedance increases as XL increases with frequency. Hence increasing circuit impedance will only accompany increasing XC below resonance (as frequency decreases).
____
Below resonance, |XL| < |XC|, so XC dominates series impedance. Above resonance, the reverse is true.
a toddler who can recognize herself in a mirror is more likely to be ________in her daycare class.
A toddler who can recognize herself in a mirror is more likely to be confident in her daycare class. Explanation: A toddler who can recognize herself in a mirror is more likely to be confident in her daycare class.
It shows that she is developing a sense of self-awareness and is more aware of her place in the world. This can lead to increased confidence and self-esteem, which can translate to better social skills and interactions with others in her daycare class.
In addition, the ability to recognize oneself in a mirror is an important developmental milestone that typically occurs around 18-24 months of age. This is an important sign of healthy cognitive and social-emotional development, and can have a positive impact on the child's overall well-being.
Overall, the ability to recognize oneself in a mirror is an important aspect of a toddler's development, and can have positive implications for their social, emotional, and cognitive growth.
It is a sign of increasing self-awareness and confidence, and can help children develop healthy relationships with others in their daycare class.
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What unit of electricity is used as a signal for a computer?
Answer:
A power supply unit (PSU) converts mains AC to low-voltage regulated DC power for the internal components of a computer. Modern personal computers universally use switched-mode power supplies
Answer:
Volt is the SI (Standard International) unit of electrical potential of the..
Explanation:
I really need help on this!
Which of the following is a term for a comparison between product metrics and values to industry standards and competitions metrics and values?
A: ideal value
B: competitive analysis
C: benchmark
D: marginally accepted value
How can technology interfere with good study habits?
Answer:
the third anwser is right on edgeinuity
Explanation:
Answer:
Technology can pull students’ focus away from their tasks.
Explanation:
(a) Consider a noisy channel between a sender and a receiver where the data link layer uses CRC (Cyclic Redundancy Check) for error detection based on a 4-bit generator: 1101. If the receiver receives a frame containing bit sequence 111001000, will the frame be discarded by the receiver? Show reasons and details in favor of your answer. A simple answer of ‘yes’ or ‘no’ without showing the details will receive no score.
(b) Find the number of collisions after which, in CSMA/CD protocol, the NIC can make a binary exponential delay of at most 1536 bit times. (c) Write down 3 cases where TDMA based protocols are preferred over CSMA/CA based ones
Yes, the receiver will discard the frame. Let's perform the CRC calculation for the bit sequence 111001000 with the generator 1101. The first bit in the sequence is a 1, so we take the first 4 bits (1110) and XOR them with the generator (1101) to get the remainder 001.
We then drop the first bit (1) and append the remainder (001) to get the new bit sequence 110010001. We now perform the same process with this new sequence and the same generator. Taking the first 4 bits (1100) and XORing with the generator (1101) gives us the remainder 001. Dropping the first bit (1) and appending the remainder (001) gives us the new bit sequence 10010001.
b) The number of collisions after which, in CSMA/CD protocol, the NIC can make a binary exponential delay of at most 1536 bit times is 10. The binary exponential backoff algorithm doubles the delay time after each collision until a maximum delay time of 1023 slots is reached. After the 10th collision, the delay time would be 1024 slots, which is greater than 1536 bit times. Therefore, the NIC would make a delay of at most 1536 bit times.
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For circuit shown, determine the total circuit current.
100 ΩξR,
R, S250 Ω
24 ν -
350 ΩξR,
R, 200 Ω
Answer:
I don't know the answer but you can download Ga u t h math to answer that
Explanation:
no spacing it is just can't lay aside
Determine the normal stress and shear stress acting on the inclined plane ab. Solve the problem using the stress transformation equations. Suppose that τ = 5. 5 ksi
The normal stress on the inclined plane ab is σ = 2.0625 ksi and the shear stress on the inclined plane ab is τ = 1.375 ksi.
How did we get the values?Determining the normal stress and shear stress acting on the inclined plane ab, use the stress transformation equations.
The stress transformation equations relate the normal stress, σ, and shear stress, τ, on an inclined plane with the corresponding normal and shear stresses acting on a plane perpendicular to the inclined plane. The equations are:
σ = σn cos²θ + σs sin²θ ± 2τnsinθcosθ
τ = (σn - σs) sinθcosθ ± τn cos²θ ± τs sin²θ
where θ is the angle between the inclined plane and the plane of reference, σn and σs are the normal stresses acting on the plane of reference, τn and τs are the shear stresses acting on the plane of reference, and τns is the shear stress acting on the inclined plane.
Given that τ = 5.5 ksi and σ and τ are to be determined on the inclined plane ab. Assume a plane of reference perpendicular to the inclined plane ab with angle θ in between.
The angle θ between the inclined plane and the plane of reference is the complement of the angle of inclination, so θ = 90° - 30° = 60°.
Assuming that there are no normal stresses acting on the plane of reference, so σn = 0. Therefore, the stress transformation equations simplify to:
σ = σs sin²θ ± 2τnsinθcosθ
τ = (σs/2) ± τn cos²θ ± (τ/2)sin²θ
Solve for σs and τn by using the given value of τ and the fact that there are no normal stresses acting on the plane of reference:
τ = τns = 5.5 ksi
σs = τ/2 = 2.75 ksi
τn = 0
Substitute these values into the stress transformation equations to obtain the normal stress and shear stress on the inclined plane ab:
σ = σs sin²θ = 2.75 ksi sin²60° = 2.75 ksi (0.75) = 2.0625 ksi
τ = (σs/2) ± τn cos²θ ± (τ/2)sin²θ = 2.75 ksi/2 = 1.375 ksi
Therefore, the normal stress on the inclined plane ab is σ = 2.0625 ksi and the shear stress on the inclined plane ab is τ = 1.375 ksi.
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