The stimulated emission of radiation in a gas or solid state laser can be achieved by A. Increasing external pumping power or energy. B. Increasing population inversion in the active medium. C. Selecting an active medium with a 4-level energy system. D. Using a resonator with two glasses coated with highly reflectance films.

Answers

Answer 1

The stimulated emission of radiation in a gas or solid-state laser can be achieved by increasing external pumping power or energy. Therefore, the correct answer is option A.

Stimulated emission is one of the fundamental processes that occur in lasers to generate coherent light. It involves the release of photons by atoms or molecules in an excited state. The options provided in the question highlight different factors that contribute to achieving stimulated emissions.

A. Increasing external pumping power or energy: This refers to providing additional energy to the active medium of the laser, such as by increasing the electrical or optical power input. This excites the atoms or molecules, promoting stimulated emission.

B. Increasing population inversion in the active medium: Population inversion occurs when the number of atoms or molecules in the excited state exceeds the number in the ground state. This can be achieved by various methods, including optical pumping or electrical discharge, to populate the higher energy levels and create a significant population inversion.

C. Selecting an active medium with a 4-level energy system: The energy levels of the active medium play a crucial role in laser operation. A 4-level energy system refers to having four distinct energy levels, which allows for efficient population inversion and stimulated emission.

D. Using a resonator with two glasses coated with highly reflective films: A resonator is an essential component of a laser that provides feedback and amplification of the emitted light. By using two glasses coated with highly reflective films as the mirrors of the resonator, the light can be reflected back and forth, increasing the chances of stimulated emission and enhancing the laser output.

In summary, achieving stimulated emission in a laser involves factors such as increasing pumping power, creating population inversion, selecting the appropriate energy system, and utilizing a resonator with highly reflective mirrors. These elements collectively contribute to the efficient generation of laser light.

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Related Questions

calculate the input impedance for the network in the figure, when r1 = 14 ω and jxl1 = j14 ω.

Answers

The input impedance for the network in the figure is j7 Ω.

The network given in the question is as follows:

We have to calculate the input impedance for the network given in the question when r1 = 14 ω and jxl1 = j14 ω.

The impedance of a circuit is the combination of resistance, inductance, and capacitance. The impedance of a circuit is a measure of the circuit's resistance to current flow when a voltage is applied.

Input impedance is the impedance seen at the input terminals of a circuit. The circuit's input impedance is the impedance it offers to an incoming signal.

To calculate the input impedance for the given network, we need to find the impedance for the components connected in parallel, i.e., R1 and Xl1.

Input impedance, Zin = V/I

Where V is the voltage applied to the circuit and I is the current flowing through the circuit.

Impedance of R1:ZR1 = R1 = 14 Ω

Impedance of XL1:XL1 = j14 Ω

The equivalent impedance of R1 and XL1 in parallel is:

Zeq = (XL1 R1) / (XL1 + R1) = (j14 × 14) / (j14 + 14) = (j196 / 28) = j7

Therefore, the input impedance for the network in the figure is j7 Ω.

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How did engineers help to create a ceiling fan

Answers

Answer:

The electric ceiling fan was invented in 1882 by engineer and inventor, Philip Diehl. He had earlier invented an electric sewing machine and adapted the motor from this invention to create the ceiling fan. He called his invention the “Diehl Electric Fan” and it was such a success that he soon had many other people competing with him.

Explanation:

Pls answer and I will give a like!

Pls answer and I will give a like!

Answers

Answer:

a

Explanation:

A 280 km long pipeline connects two pumping stations. It is desired to pump 0.56 m3/s of oil through a 0.62 m diameter line, the discharge station is 250 m lower in elevation than the upstream station, and the discharge pressure is to be maintained at 300 kPa. The oil has a dynamic viscosity of 3.645 x 10-3 Pa·s and a density of 810 kg/m3. The pipe is constructed of commercial steel and the inlet pressure may be taken as 1 atmosphere. Considering the mechanical-energy friction loss Ff, determine the power required to pump the oil if the power efficiency is 70%. Develop a sketch of the piping system considered.
Ignore energy losses due to contraction, expansion & 90° bends!!!

Answers

Can u answer myn and if u do I’ll do urs

Electrical Circuit question..

Electrical Circuit question..

Answers

Answer:

Cool.

Explanation:

5. Refrigeration refers to space temperatures that are below

What the correct answer?

Answers

Explanation:

The term refrigeration means cooling a space, substance or system to lower and/or maintain its temperature below the ambient one (while the removed heat is rejected at a higher temperature). In other words, refrigeration is artificial (human-made) cooling.

Refrigeration, is the act of removing undesirable heat from one thing, substance, or space and transferring it to another object, substance, or space.

What is refrigeration?

Refrigeration refers to the process of chilling an area, material, or system in order to decrease and or keep its temperature below that of the surrounding environment.

Refrigeration, sometimes known as chilling, is the act of removing undesired heat from one item, substance, or area and transferring it to another.

The temperature can be lowered by using ice, snow, cooled water, or mechanical refrigeration to remove heat.

Hence,refrigeration, is the act of removing undesirable heat.

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how would i be able to make a simple mechanism that will feed my bird in a pull of a lever, and know when to refill itself?

Answers

Answer:  Take two cups. ...

Tie a string to one hole on a cup, then thread it through the hole on one end of a stick.

Tie the end of the string to the other hole in that cup.

Now, take the second cup. ...

Hold the stick on its side, with the cups hanging down. ...

Put weights in the cups to balance.

Explanation:

the highway department is to design a roadway over a swamp area. the swamp consists of very soft fine-grained soils obviously saturated. the basic idea is to build a relatively small embankment above the flood level. how would you propose to build the embankment, fast, slow, or in stages? explain.

Answers

I'd like to propose that the embankment be built in stages. Because of the possibility of abrupt coloase of structure in swampy places. Soil carrying capacity is extremely low in those places. You must first densify the soil and make it acceptable using various procedures such as grouting, vibrification, restricting, and so on. These types of jobs are critical during the earliest stages of embankment development. After that, we can begin our construction work.

What is soil?

Soil, often known as earth or soil, is a complex mixture of organic matter, minerals, gases, liquids, and creatures that support life. Some scientific definitions distinguish dirt from soil by limiting the former term to displaced soil only. Soil is made up of two phases: a solid phase of minerals and organic matter and a porous phase that retains gases and water. As a result, soil is a three-state system composed of solids, liquids, and gases. Soil is the result of various elements interacting throughout time, including climate, relief, creatures, and the parent components of the soil.

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What is the first step that needs to be taken when troubleshooting a network incident?a. Document the incidentb. Identify the problemc. Remediate the incidentd. Establish a theory of the incident

Answers

During troubleshooting a network incident, the first step is to identify the problem.

How is a network connection troubleshooted?

Go to Settings > Network & Internet > Status by clicking the Start button. Choose Network troubleshooter from the list under Modify your network settings. By according to the troubleshooter's recommendations, see if the problem has been fixed.

What constitutes a troubleshooting fundamental?

The following are the steps in the troubleshooting process:

Determine the issue.Create a likely cause theory.To ascertain the cause, test the theory.Make a plan or action to tackle the issue and put the solution into practice.Verify the complete system's functionality, and if necessary, take preventative action.

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Q2. Considering network design model PDIOO, answer the following: a. What are the 4 types of network conversion? Which one is the WORST and why? b. Talk about training as part of implementation stage.

Answers

The 4 types of network conversion are Parallel, Phased, Cut-over, and Pilot. Among these types, the Cut-over is the worst because it is risky and may cause significant interruptions to network services. Moreover, training is an essential part of the implementation stage. It is necessary to make sure the network is designed, installed, and operated in a consistent manner by the staff.

PDIOO is the network design model. It stands for Plan, Design, Implement, Operate, and Optimize. Network conversion has 4 types. They are the following: Parallel, Phased, Cut-over, and Pilot. Among these types, the worst type of network conversion is Cut-over. The cut-over type of network conversion is the riskiest of all the four types. In the case of this type, the entire existing system is replaced by the new one, making the cut-over a critical point in the whole process. This conversion may also result in significant interruptions to network services if any failures occur.

Training is an essential part of the implementation stage. It is necessary to make sure the network is designed, installed, and operated in a consistent manner by the staff. It is necessary to provide training to network support personnel as part of the implementation process. It is essential to develop training plans for the technical staff, the help desk support staff, the operations staff, and the end-users of the network.

This training should be provided in different areas. These areas should include network monitoring, device management, operating system updates, data backup and recovery procedures, network security, network policy, network administration, network protocols, and so on. The success of the network's implementation depends upon how well trained the staff is.

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Hot batt bus powers what ignition components

Answers

The exact components that are powered by the hot battery bus may vary depending on the specific aircraft and its configuration.

We have,

The hot battery bus is an electrical circuit in an aircraft that is typically powered by the aircraft's battery or an auxiliary power unit (APU) and provides electrical power to critical aircraft systems, including certain ignition components.

Specifically, the hot battery bus may provide power to the primary ignition system, which is responsible for initiating combustion in the engine.

This includes components such as the ignition switch, magneto, spark plugs, and associated wiring and circuitry.

In addition to the primary ignition system, the hot battery bus may also power other critical aircraft systems, such as avionics, flight instruments, and emergency lighting.

Thus,

The exact components that are powered by the hot battery bus may vary depending on the specific aircraft and its configuration.

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What is the acceleration of a 0.8 kg vehicle powered by 0.07 N of force?

Answers

Using the Newton's second law of motion we will see that the acceleration is  0.0875 m/s^2.

What is the acceleration of the vehicle?

The acceleration of a vehicle is determined by the force acting on it and its mass, as described by Newton's second law of motion:

F = m * a

where F is the force acting on the object, m is the mass of the object, and a is the resulting acceleration.

In this case, the force acting on the vehicle is 0.07 N, and the mass of the vehicle is 0.8 kg. Substituting these values into the equation above, we get:

0.07 N = 0.8 kg * a

Solving for a, we get:

a = 0.07 N / 0.8 kg

a = 0.0875 m/s^2

Therefore, the acceleration of the 0.8 kg vehicle powered by 0.07 N of force is 0.0875 m/s^2.

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What is your creative solution for clean, sustainable, and accessible energy?

Answers

Plant power and solar power or air power which is kinda a infinite power source

a motor compressor unit with a rating of 32 amps is protected from over loads by a separate overload relay selected to trip at not more than amps.

Answers

It sounds like you are asking about a motor compressor unit that is protected from overloading by a separate overload relay.

A particular amount of amps of current are chosen to trigger the overload relay.

Selecting an overload relay with a trip point that is appropriate for the motor rating will help to guarantee that the motor compressor unit is protected appropriately. Given that the motor in this instance has a 32 amp rating, the overload relay should be set to trigger at currents no greater than 32 amps. By doing this, you can make sure that the overload relay trips and turns the engine off before it sustains damage from too much current.

It's crucial to regularly check the overload relay to make sure it's working properly.

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to cool a given room it is necessary to supply 4 ft3 /s of air through an 8-in.-diameter pipe. approximately how long is the entrance length in this pipe?

Answers

To cool a given room it is necessary to provide 4 ft³/s of air through an 8-inches diameter pipe, for this Entrance length in this pipe = 17.7 ft

Q = 4ft³/s

Diameter = D = 8 inches

Entrance length in this pipe = \(l_{e}\) = ?

By using flow rate formula:

V = Q/A

V= Q/ π/4*D²

= 4ft³/s / π/4 (8/12 ft)²

V= 11.5 ft/s

Thus, with ν = 1.57 x 10⁻⁴ft²/s (value from table)

Re = VD/ν

Re = 11.5 ft/s (8/12 ft)/1.57x10⁻⁴ft²/s

Re = 48,800 > 4000 (based on the criteria)

so, the flow is turbulent

Hence,

\(l_{e} / D\) = \(4.4 R_{e}^{1/6}\)

\(l_{e}\) = 4.4 (48,800)\(^{1/6}\) (8/12)

\(l_{e}\) = 17.7 ft

Entrance Length of an 8-inch diameter pipe = 17.7 ft

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Could someone please help me

Could someone please help me

Answers

The angular velocity is ω = VA/L and the qngular acceleration is α = -g/L

How to calculate the value

The velocity of end A can be expressed as:

VA = Lω

where L is the length of the bar and ω is the angular velocity.

The acceleration of end A can be expressed as:

aA = Lα

where L is the length of the bar and α is the angular acceleration.

We can see from the diagram that the acceleration of end A is equal to the acceleration due to gravity, minus the centripetal acceleration.

aA = g - Lω²

Substituting VA = Lω into the equation for aA, we get:

g - Lω² = Lα

Solving for ω, we get:

ω = VA/L

Substituting ω = VA/L into the equation for aA, we get:

α = -g/L

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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.

The steel shaft has a diameter of 40 mm and is fixed at its ends A and B . If it is subjected to the

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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QUESTION 2
After two technicians examine a broken and disintegrated DPF, Technician A says that the filter damage was caused by water
contamination of an ash-loaded filter. Technician B says that the filter was damaged by back-to-back regenerations that occurred
too frequently. Who is correct?
O a. Technician A
O b. Technician B
O c. Both Technician A and Technician B.
O d. Neither Technician A nor Technician B
QUESTION 3
Technician A says that the diesel exhaust oxidation catalysts used by diesel engines are like the ones that have been used in
automobiles for the last 2 decades. Technician B says that diesel exhaust oxidation catalysts store noxious emissions in the substr
when the exhaust temperatures are low. Who is correct?
O a. Technician A
O b. Technician B
O c. Both Technician A and Technician B
O d. Neither Technician A nor Technician B

Answers

Answer:

2:C 3:B

Explanation:

2. It is difficult to determine who is correct without additional information or context about the situation. Both Technician A and Technician B offer plausible explanations for the cause of the filter damage, and it is possible that both factors contributed to the problem. Therefore, the correct answer is (c) Both Technician A and Technician B.

3. Technician B is correct. Diesel exhaust oxidation catalysts do store noxious emissions in the substrate when the exhaust temperatures are low. This is known as "cold start emissions," and the stored emissions are later released when the catalyst reaches its operating temperature. Technician A is incorrect in stating that diesel exhaust oxidation catalysts are like the ones used in automobiles for the last 2 decades, as diesel engines have different emissions profiles and require different types of catalysts. Therefore, the correct answer is (b) Technician B.

Counter argument for why engineers dont make a positive change in the world.​

Answers

Answer:

They don't make a positive change in the world because they have made mistakes that aren't able to be made fixed and there are a lot of engineers who haven't study enough and know the important basis of coming to engineer.

what is the direct current generator​

Answers

Answer:

A direct-current (DC) generator is a rotating machine that supplies an electrical output with unidirectional voltage and current.

Explanation:

Hope this helps

on sheet e6, there are six 20-amp 120-volt receptacles shown along column line c, between columns 3 and 4. what is the proper mounting height for these receptacles? (choose all that apply.)

Answers

The proper mounting height for receptacles can vary depending on the application and local building codes. However, a common recommended mounting height for receptacles in a commercial setting is 18 inches above the finished floor to the center of the receptacle.

Therefore, for the six 20-amp 120-volt receptacles shown along column line c, between columns 3 and 4 on sheet e6, the proper mounting height would be 18 inches above the finished floor to the center of each receptacle.

So the possible answers are:

18 inches above the finished floor to the center of each receptacle.

It's not possible to determine the exact mounting height without additional information about the specific building codes and requirements for the application.

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how to answer for computer science quora how do your interests directly connect with cornell engineering? if you have an intended major, what draws you to that department at cornell engineering? if you are unsure what specific engineering field you would like to study, describe how your general interest in engineering most directly connects with cornell engineering. it may be helpful to concentrate on one or two things that you are most excited about\.\* (250 words)

Answers

Focus primarily on highly precise specifics of what Cornell offers and how it matches with your interests and values. You can regard this as a "Why us?" essay with some optional "Why major" spice.

How to write essay ?Cornell is fundamentally a research institution, and I am fundamentally a researcher. The Collective Embodied Intelligence Lab would be the ideal place for me to put what I have learned from my own work in that area to use while learning from Dr. Petersen and her ground-breaking research in termite-inspired construction robots. The lab focuses on the control of multi-agent robotic systems, especially drawing inspiration from insect swarm mechanics. Cornell is known for its research, but what truly stood out to me was its distinct dedication to project teams. I discovered I wanted to join every team after doing my homework on them. Consider Baja; the idea of creating an off-road car from scratch is comparable to FTC competitions. Even though I have a strong foundation in CAD, wiring, and chassis construction, I'm eager to tackle more complex issues with even more room for creativity.

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A circuit has two resistors in parallel, each resistor is 6 ohms. This circuit is connected to a single resistor of 6 ohms, to form a series-parallel circuit. What is the total resistance of the circuit?

Answers

The tatal resistance of the series-parallel circuit with two resistor connected in parallel which combination is connected in series to a single resistor is 9 ohms.

What is a resistance?

This can be defined as the opposition to current flow in a circuit.

To calculate the total resistance, first we need to find the total resistance of the parallel resistor.

For parallel,

R' = (R₁R₂)/(R₁+R₂)............Equation 1

Where:

R' = Total resistance of the parallel resistor.

From the question,

Given:

R₁ = 6 ohmsR₂ = 6 ohms

Substitute these values into equation 1

R' = (6×6)(6+6)R' = 3 ohms.

Finally, we combine the effective parallel resistance in series to the single resistance to the the total resistance of the circuit.

Rt = R'+R₃.................. Equation 2

Where:

Rt = Total resistance of the circuit.

From the question,

R' = 3 ohmsR₃ = 6 ohms

Substitute these values into equation 2

Rt = 3+6Rt = 9 ohms.

Hence, the total resistance of the circuit is 9 ohms.

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When a cellular telephone sends a text message, the cell carrier encodes the text message and transmits the message to the receiving cellular telephone. The encoded text message is the data of the transmission.

In addition to transmitting the data, the cell carrier company also stores metadata. The metadata of the text message includes the time the message was sent, the phone number of the sender, and the phone number of the receiver.

For which of the following goals would it be more useful to computationally analyze the metadata instead of the data?

I. Estimate the number of texts that will be sent next month
II. Determine the most frequently used emoji in text messages
III. Determine if two phones have been in contact in the last week

a) I only

b) II only

c) I and III

d) I, II, and III

Answers

The answer is c) I and III.

Metadata analysis is useful for estimating future text volumes and tracking communication patterns.

Which goals benefit from analyzing metadata?

Computational analysis of metadata, rather than the data itself, is more useful for estimating the number of texts that will be sent next month (goal I) and determining if two phones have been in contact in the last week (goal III). Metadata provides valuable information such as the time the message was sent, phone numbers of the sender and receiver, which can be used to analyze patterns, trends, and connections between devices.

For goal I, by analyzing metadata from previous months, trends can be identified to estimate the number of texts that will likely be sent next month. This information can help the cell carrier allocate resources and plan accordingly.

For goal III, analyzing metadata allows the identification of communication patterns between devices. By examining the timestamps and phone numbers associated with the messages, it is possible to determine if two phones have been in contact within a specified time frame, which can be useful for various purposes such as contact tracing or investigating connections between individuals.

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2. In a certain Village in eastern Uganda, residents use on average 1.5 Kg per inhabitant of
wood per day in a traditional stove of 12% efficiency. If the village has 200 in habitants,
Find,
i.
The
total mass of wood consumed daily.
ii.
The Energy demand of the village in KWh.
iii.
The actual energy consumption of the village in KWh.
iv.
If an investor would like to provide this village with a new energy converter of 30%
efficiency, how many Kilograms of wood will be required per day

Answers

probably alot lol

Explanation:

it probably is

A stone is catapulted at time t = 0, with an initial velocity of magnitude 21.1 m/s and at an angle of 39.9° above the horizontal. What are the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t = 1.08 s? Repeat for the (c) horizontal and (d) vertical components at t = 1.75 s, and for the (e) horizontal and (f) vertical components at t = 5.09 s. Assume that the catapult is positioned on a plain horizontal ground.

Answers

Answer:

(a) X = 17.48 m

(b) Y = 8.903 m

(c) X = 28.33 m

(d) Y = 8.68 m

(e) X = 44.68 m

(f) Y = 0 m

Explanation:

Given;

magnitude of initial velocity, v = 21.1 m/s

angle of projection, θ = 39.9°

the horizontal component of the velocity, \(v_x = vcos \theta\)

\(v_x = 21.1(cos 39.9^0) = 16.187 \ m/s\)

the vertical component of the velocity, \(v_y = vsin \theta\)

\(v_y = 21.1(sin 39.9^0) = 13.535 \ m/s\)

(a)  the horizontal components of its displacement;

\(X = v_xt + \frac{1}{2} gt^2\)

gravitational influence on horizontal direction is negligible, g = 0

\(X = v_xt \\\\X = (16.187)(1.08)\\\\X = 17.48 \ m\)

(b) the vertical components of its displacement;

\(Y = v_yt + \frac{1}{2} gt^2\\\\Y = (13.535*1.08) + \frac{1}{2} (-9.8)(1.08)^2\\\\Y = 14.618 -5.715\\\\Y = 8.903 \ m\\\)

(c) the horizontal components of its displacement;

\(X = v_xt\\\\ X = (16.187)(1.75)\\\\X = 28.33 \ m\)

(d) the vertical components of its displacement;

\(Y = v_yt + \frac{1}{2} gt^2\\\\Y = (13.535 *1.75) + \frac{1}{2} (-9.8)(1.75)^2\\\\Y = 8.68 \ m\)

(e)  the horizontal components of its displacement;

\(X = v_xt \\\\X = (16.187*5.09)\\\\X = 82.39 \ m\\\)

(f) the vertical components of its displacement;

\(Y = v_yt + \frac{1}{2}gt^2\\\\ Y = (13.535*5.09)+ \frac{1}{2}(-9.8)(5.09)^2\\\\Y = -58.1 \ m\)

this displacement is not possible because it is beyond zero vertical level; it shows that the stone will hit the ground before 5.09 s.

When the stone hits the ground Y = 0 m

At zero vertical displacement (Y = 0 m), the time at that position will be calculated as;

\(Y = v_yt+\frac{1}{2}gt^2\\\\0 = (13.535t) + \frac{1}{2}(-9.8)t^2\\\\0= 13.535t - 4.9t^2\\\\0 = t(13.535-4.9t)\\\\t = 0 \ \ or \\\\13.535-4.9t = 0\\\\4.9t = 13.535\\\\t = 2.76 \ s\)

The horizontal displacement at this time is given by;

X = vₓt

X = (16.187 x 2.76)

X = 44.68 m

For the beam loaded as shown in Fig Q2a. perform the following task:
Calculate the support reactions at A and E;
(i)
Draw the shear force diagram for the beam showing all important
values;
>
(iii)
Draw the bending moment diagram for the beam showing all
important values.
6 kN
10 KN
2 kN/m
B
D
1 m
1 m
1 m
1 m

Answers

Answer:

a

Explanation:

aaaaaa

2. A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit

of surface area is twice as great for the for the hemisphere as it is for the cylindrical side wall. Determine the dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction.​

Answers

An extremum is a point where the function has its highest or lowest value, and at which the slope is zero.

The dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum is as follows;

Height of cylinder = 2 × Radius of cylinder

Reason:

The given parameters are;

Form of silo = Cylinder surmounted by a hemisphere

Cost of construction of hemisphere per square unit = 2 × The cost of of construction of the cylindrical side wall

Required:

The dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum

Solution:

The fixed volume of the silo, V, can be expressed as follows;

\(V = \pi \cdot r^2 \cdot h + \dfrac{2}{3} \cdot \pi \cdot r^3\)

\(h = \dfrac{V - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 }\)

Where;

h = The height of the cylinder

r = The radius of the cylinder

The surface area is, Surface Area = 2·π·r·h + 2·π·r²

The cost, C = 2·π·r·h + 2×2·π·r² = 2·π·r·h + 4·π·r²

Therefore;

\(C = 2 \times \pi \times r\times \dfrac{V - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 } + 4 \cdot \pi \cdot r^2 = \dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r}\)

\(C = \dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r}\)

At the minimum value, we have;

\(\dfrac{dC}{dr} =0 = \dfrac{d}{dr} \left(\dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r} \right) = \dfrac{16 \cdot r^3 \cdot \pi - 6 \cdot V}{3 \cdot r^2}\)

Which gives;

16·π·r³ = 6·V

\(V = \dfrac{16 \cdot \pi \cdot r^3}{6} = \dfrac{8 \cdot \pi \cdot r^3}{3}\)

Which gives;

\(h = \dfrac{\dfrac{8 \cdot \pi \cdot r^3}{3} - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 } = 2 \cdot r\)

h = 2·r

The height of the silo, h = 2 × The radius, 2

Therefore, the dimensions to be used if the volume is fixed and the cost is to be kept to a minimum is, height, h = 2 times the radius

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How does the example of the automobile support the statement that most technological development has been evolutionary, the result of a series of refinements to a basic invention?

Answers

Explanation:

In the future automobiles will be more complex and safer to use. They are currently working on how to create an auto pilot where the navigation system guides the car to its destination and the driver doesn't have to do anything. We have the technology now to be able to develop easier and safer ways to drive.

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what is a home that has its own roof, foundation, and a wall that extends from the roof through the foundation

Answers

Fire wall is a home that has its own roof, foundation, and a wall that extends from the roof through the foundation.

What is a Fire wall?

This is known to be a form of rated assembly that ranges from the foundation to and via the roof of a building to lower the rate of fire spread.

Note that, Fire wall is a home that has its own roof, foundation, and a wall that extends from the roof through the foundation.

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