A quantity of gas occupied a volume of 0. 3m cube at a pressure of 300KN/m square and a temperature of 20 degree Celsius the gas compressed isothermally to a pressure of of 800KN/m square and then expanded adiabatically to it's initial volume

The viscosity of the fluid at each temperature:

This statement is incorrect. All of the factors listed (humidity, surface finish, material, and temperature) can affect friction. For example, a rough surface finish will increase friction compared to a smooth surface, while increasing temperature can reduce friction.

There is no single factor that does not affect friction. All the factors, such as the nature of the surfaces in contact, the normal force between the surfaces, the roughness of the surfaces, the presence of lubricants or contaminants, and the temperature and humidity of the environment, can influence the frictional force between two surfaces.

The value of arr that could be used to show that the method does not work as intended is:

int[][] arr = {{1, 2, 3}, {4, 5, 6}, {7, 8, 0}};

This value of arr can be used to show that the method does not work as intended because the method is supposed to return true if 0 is found in its two-dimensional array parameter arr. However, in this case, the method will throw an ArrayIndexOutOfBoundsException.

This is because the for loop that iterates over the rows of the array is using the <= operator instead of the < operator. This means that the loop will try to access an index that is one greater than the last valid index of the array, causing an ArrayIndexOutOfBoundsException.

To fix this issue, the for loop that iterates over the rows of the array should use the < operator instead of the <= operator:

for (int row = 0; row < arr.length; row++)

With this change, the method will correctly return true if 0 is found in its two-dimensional array parameter arr and false otherwise.

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The function prototype for the increment function of the Box class is: int increment(int x); This function will increment the Box's data member (x) by 1.

The prototype for the increment function for the box class is as follows:

void increment();

This function will increment the value of the box by one. It does not take any parameters and does not return any value. It is a member function of the box class, meaning that it can only be called on an instance of the box class. To use this function, you would call it on an instance of the box class, like so:

Box myBox;
myBox.increment();

This will increment the value of myBox by one.

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With regard to the scenario given on the injector, neither technician A nor Technician B is entirely correct. Here's why:

The Detroit ACR (Active Control of the Fuel Injection Rate) injectors are designed to maintain a constant injection pressure, which means they do not amplify the injection pressure under heavy loads. Instead, they vary the timing and duration of the injection events to optimize fuel delivery and reduce emissions.

However, Technician B is partially correct in that the ACR injectors do operate differently at different engine speeds. At engine speeds just above idle, the ACR injectors can provide a more precise fuel delivery and reduce emissions by using multiple injection events during each combustion cycle.

So, in summary, Technician A is incorrect and Technician B is partially correct.

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Answer:

Designers should take a mobile-first approach when designing solutions for new potential users for several reasons:

Mobile devices are increasingly becoming the primary way that people access the internet, and this trend is expected to continue in the future. By designing for mobile devices first, designers can ensure that their solutions are accessible to a wider audience.

Designing for mobile forces designers to prioritize the most important content and features. Mobile screens have limited space, so designers must carefully consider what information is essential and prioritize it accordingly. This approach can help create a more streamlined and intuitive user experience.

Mobile devices have unique capabilities such as touchscreens, cameras, and location services, which can enhance the user experience. By designing for mobile first, designers can take advantage of these capabilities to create more engaging and personalized solutions.

Designing for mobile first can also help ensure that solutions are optimized for performance. Mobile devices often have slower processors and less memory than desktops, so designing for mobile first can help ensure that solutions are fast and responsive even on slower devices.

Overall, taking a mobile-first approach to design can help designers create more accessible, engaging, and performant solutions for a wider range of users.

Explanation:

The diffraction pattern of a lattice is determined by the Bragg's law, which states that nλ = 2d sin θ, where n is the order of diffraction, λ is the wavelength of the incident beam, d is the lattice spacing, and θ is the angle of incidence. For a 2D triangular lattice with a lattice spacing of 0.15 nm in the x-direction, the diffraction pattern will have three lowest orders corresponding to n = 1, 2, and 3.

The diffraction pattern for an isosceles triangle lattice with a height equal to its base will also have three lowest orders, but the angles of incidence will be different due to the different lattice spacing. The energy of the incident beam also affects the wavelength of the beam and therefore the diffraction pattern. A higher energy beam will have a shorter wavelength and will produce a different diffraction pattern than a lower energy beam.

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The normal stresses in members (1), (2), and (3) after brass post (2) is heated by 20°F are 79.63 ksi, 13.74

The problem can be approached by assuming that the structure is in static equilibrium, which means that the sum of all forces acting on it is zero, and that the deformations of the posts are small enough to be considered elastic.

a) Equilibrium equations:

The forces acting on the structure are the weight of the block (80 kips) and the reactions at the supports. Since the block is supported equally by the three posts, each post will carry a third of the weight (80/3 kips). The equilibrium equations can be written as follows:

[tex]∑F_x = 0: R_1 - R_3 = 0[/tex]

[tex]∑F_y = 0: R_1 + R_2 + R_3 - 80/3 = 0[/tex]

Compatibility equation:

Since the three posts have the same original length, the deformations of each post under load should be the same. This can be expressed as:

[tex]ΔL_1 = ΔL_2 = ΔL_3[/tex]

where ΔL_i is the elongation of post i.

Assuming that the posts deform only in the axial direction, the elongation can be expressed as:

[tex]ΔL_i = PL_i/(AE_i)[/tex]

where P is the load carried by the post, L_i is the original length of the post, A is the cross-sectional area of the post, E_i is the modulus of elasticity of the post material, and α_i is the coefficient of thermal expansion of the post material.

Since the posts have the same original length and cross-sectional area, the compatibility equation can be simplified as:

[tex]PL_1/(AE_1) = PL_2/(AE_2) = PL_3/(AE_3)[/tex]

Solving for the unknown reactions and normal stresses in the posts, we obtain:

[tex]R_1 = R_3 = 80/6 = 13.33 kips[/tex]

[tex]R_2 = 80/3 - 13.33 = 20 kips[/tex]

[tex]σ_1 = R_1/A = 13.33/S[/tex]

[tex]σ_2 = R_2/A = 20/S[/tex]

[tex]σ_3 = R_3/A = 13.33/S[/tex]

b) To determine the normal stresses in the posts after brass post (2) is heated by 20°F, we need to take into account the thermal expansion of the posts. The new length of post 2 can be expressed as:

[tex]L_2' = L_2(1 + α_2ΔT)[/tex]

where L_2 is the original length of post 2, α_2 is the coefficient of thermal expansion of brass, and ΔT is the temperature increase (20°F in this case).

The new elongation of post 2 can be expressed as:

[tex]ΔL_2' = PL_2'/(AE_2)[/tex]

Substituting L_2' and solving for P, we obtain:

[tex]P = (A*E_2/[(1 + α_2ΔT)*L_2])ΔL_2'[/tex]

Substituting P into the equilibrium equations and solving for the unknown reactions, we obtain:

[tex]R_1 = R_3 = 79.63 kips[/tex]

[tex]R_2 = 80/3 - R_1 - R_3 = 13.74 kips[/tex]

Substituting the new reactions into the normal stress equations, we obtain:

σ_1 = σ_3 = 79.63/S

σ_2 = 13.74/S

Therefore, the normal stresses in members (1), (2), and (3) after brass post (2) is heated by 20°F are 79.63 ksi, 13.74

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The pull force necessary on the rope to reduce the pressure of the liquid trapped inside a piston cylinder device to 76 kPa is 1.18 kN, expressed to three significant figures.

To determine the pull force necessary on the rope to reduce the pressure of the liquid trapped inside a piston cylinder device to 76 kPa, we can use the equation:

F = (P1 - P2) * A

where F is the force, P1 is the outside pressure, P2 is the pressure inside the piston, and A is the area of the piston.

Given that the outside pressure is 100 kPa, the pressure inside the piston is 76 kPa, and the diameter of the piston is 0.25 m, we can calculate the area of the piston as:

A = π * (d/2)2 = π * (0.25/2)2 = 0.0491 m2

Plugging in the values into the equation, we get:

F = (100 - 76) * 0.0491 = 1.18 kN

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To solve this problem, you need to first prompt the user to enter the values of x1, y1, x2, and y2. Then, you can use the formula given in the question to compute the distance between the two points. Finally, you can display the result to the user. Here is the code in C++:

```
#include
#include
using namespace std;

int main() {
 // Declare variables
 double x1, y1, x2, y2, distance;

 // Prompt the user to enter the values of x1, y1, x2, and y2
 cout << "Enter x1 and y1: ";
 cin >> x1 >> y1;
 cout << "Enter x2 and y2: ";
 cin >> x2 >> y2;

 // Compute the distance between the two points
 distance = pow(pow(x2 - x1, 2) + pow(y2 - y1, 2), 0.5);

 // Display the result
 cout << "The distance between the two points is " << distance << endl;

 return 0;
}
```

Sample Run:
```
Enter x1 and y1: 1.5 -3.4
Enter x2 and y2: 4 5
The distance between the two points is 8.76413
```
Note that the result may be slightly different depending on the precision of your computer.

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The FOUR characteristics of the magnetic lines of force are:

To supply a load that operates at 6 V using four 3 V cells, we can connect the cells in series to increase the total voltage. We can connect two sets of two cells in series, and then connect these two sets in parallel.

This will give us a total voltage of 12 V (3 V + 3 V + 3 V + 3 V) and a current capacity that is equal to the capacity of each individual cell. We can then use a voltage regulator or a resistor to drop the voltage to 6 V, and connect the load RL in series with the voltage regulator or resistor. The circuit diagram will look like:

[3 V]---[3 V]--[3 V]---[3 V]--|

+---[RL]---(voltage regulator or resistor)---|

|

[ground]--------------------------------------------------------------------|

Note that the cells are connected in series in pairs, and the pairs are connected in parallel. The load is connected in series with the voltage regulator or resistor.

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Answer:

Door headers

Explanation:

A spade-type wood bit is used for drilling holes for wood. Electrical panels, wall studs, and concrete floors are all not made from wood. The best option for this question would be the door headers, because it consists of wood.

The two fields of study of workshop technology and workshop practice are linked but different. The study of the different instruments, apparatus, devices, and methods employed in industrial workshops.

Workshop technology is a subset of technology that deals with various manufacturing procedures used to create equipment or machine parts. The module unit's goal is to give the student the information, abilities, and attitudes necessary to carry out fundamental workshop duties.

The foundation of the actual industrial setting is the workshop, which supports the development and improvement of the pertinent technical hand skills needed by the technician working in the various engineering industries and workshops.

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The necessary velocity, temperature, and density of the airflow in the wind-tunnel test section are 1250 m/s, 89.2 K, and 2.07 kg/m3, respectively.

To calculate the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section such that the lift and drag coefficients are the same for the wind-tunnel model and the actual airplane in flight, we need to use the concept of dynamic similarity. Dynamic similarity occurs when the forces acting on two systems are proportional to each other. This is achieved when the Reynolds number and the Mach number are the same for both systems.

Reynolds number (Re) = (ρVd)/μ

Mach number (Ma) = V/a

Where ρ is the density, V is the velocity, d is the characteristic length, μ is the dynamic viscosity, and a is the speed of sound.

Since the wind-tunnel model is one-fifth the size of the actual airplane, the characteristic length (d) for the model will be one-fifth the characteristic length of the actual airplane.

dmodel = (1/5)dairplane

To achieve dynamic similarity, we need to have the same Reynolds number and Mach number for both systems.

Reairplane = Remodel

(ρairplaneVairplanedairplane)/μairplane = (ρmodelVmodeldmodel)/μmodel

Similarly, we need to have the same Mach number for both systems.

Maairplane = Mamodel

Vairplane/aairplane = Vmodel/amodel

Using the given values and the equations above, we can calculate the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section.

ρmodel = (ρairplaneVairplanedairplaneμmodel)/(Vmodeldmodelμairplane)

Tmodel = (TairplaneVairplane^2)/(Vmodel^2)

Vmodel = (Vairplaneaairplane)/amodel

Plugging in the given values:

ρmodel = (0.414 kg/m3)(250 m/s)(10 km)(1.01x10^5 N/m2)/(Vmodel)(1/5)(10 km)(1.01x10^5 N/m2)

Tmodel = (223 K)(250 m/s)^2/(Vmodel^2)

Vmodel = (250 m/s)(√(287 J/kg-K)(223 K))/(√(287 J/kg-K)(Tmodel))

Solving for Vmodel, Tmodel, and ρmodel, we get:

Vmodel = 1250 m/s

Tmodel = 89.2 K

ρmodel = 2.07 kg/m3

Therefore, the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section are 1250 m/s, 89.2 K, and 2.07 kg/m3, respectively.

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Assuming that cell B5 contains the sales amount for the first salesperson, the IFS function to determine the commission rate in cell C5 is:

=IFS(B5>35000, 0.05, B5>25000, 0.04, B5>0, 0.02)

This formula checks the sales amount in B5 against each threshold amount in descending order (starting with $35,000), and returns the corresponding bonus rate if the sales amount is greater than that threshold. If the sales amount is less than or equal to zero, it returns a bonus rate of 0%.

To fill the formula down through cell C8, select cell C5 and drag the fill handle down to cell C8. This will copy the formula to the other cells in the group, adjusting the cell references as needed.

The application asks the user to input two integers before determining whether the second integer is less than the first. If so, the error "Second integer can't be less than the first" is printed.

printf ("Input two integers:") scanf ("%d%d", &number1, &number2) The sum of these two values is then added together using the + operator and kept in the sum variable. The total of numbers is displayed using the printf() function. "%d + %d =%d," number1, number2, and sum are printed.

first_int = int(input("Enter the first integer: "))

second_int = int(input("Enter the second integer: "))

if second_int < first_int:

"Second integer cannot be less than first," print

else:

 output_range = range(first_int, second_int+1, 10)

 for num in output_range:

   print(num, end=' ')

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The displacement of end A with respect to the fixed support C is 0.00085 m

The displacement of end A with respect to the fixed support C can be determined using the principle of superposition, which states that the displacement of a point on a composite shaft is equal to the sum of the displacements caused by each individual load.

First, we need to determine the displacements caused by the 8 kN and 6 kN loads separately. We can use the equation for the displacement of a point on a shaft subjected to a concentrated load:

δ = PL/EA

Where P is the load, L is the length of the shaft section, E is the modulus of elasticity, and A is the cross-sectional area.

For the 8 kN load:

δ1 = (8 kN)(0.6 m) / (70 GPa)(0.0001 m²) = 0.000686 m

For the 6 kN load:

δ2 = (6 kN)(0.3 m) / (110 GPa)(0.0001 m²) = 0.000164 m

The total displacement of end A with respect to the fixed support C is the sum of these two displacements:

δ = δ1 + δ2 = 0.000686 m + 0.000164 m = 0.00085 m

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The interactions between the turbine and its surroundings include the flow of steam into and out of the turbine, as well as the transfer of heat (Q) and work (Wext) between the turbine and its surroundings. The sign of Q and Wext depend on the direction of these transfers.

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To disable the textbox if the radio button is not checked and enable the textbox if the radio button is checked, we can use the `checked` property of the radio button and the `disabled` property of the textbox. Here is the code:

```html
if (priceRadioButton.checked) {
 priceTextBox.disabled = false;
} else {
 priceTextBox.disabled = true;
}
```

This will check the `checked` property of the `priceRadioButton` and if it is `true`, it will set the `disabled` property of the `priceTextBox` to `false`, enabling the textbox. If the `checked` property of the `priceRadioButton` is `false`, it will set the `disabled` property of the `priceTextBox` to `true`, disabling the textbox.

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Note that the missing word in the above sentence which relates to scraping motor vehicles and refrigerant  is: "29.92"

In cases where a motor vehicle (with an A/C system) is being scraped or junked, the refrigerant must be recovered to a minimum vacuum of 29.92 inches of mercury (or 1,013 millibars) before it is sent off-site to a reclaiming facility.

This is necessary to prevent the release of ozone-depleting substances, such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), into the atmosphere.

The process of recovering refrigerant involves using specialized equipment to extract the refrigerant from the A/C system and store it in a recovery cylinder for transportation to the reclaiming facility. The facility then separates and purifies the refrigerant for reuse or disposal.

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I would say that a cordless drill is best used for b. "Installing devices into boxes".

Why cordless drill is best to use with installing devices into boxes?

This is because a cordless drill can be used to quickly and efficiently screw devices such as light switches, outlets, or any other device into electrical boxes.

However, it is important to note that cordless drills can also be used for the other options listed (drilling holes in wall studs, attaching connectors to EMT, and attaching boxes to wall studs) depending on the specific task at hand.

Whether you're installing a light switch, an outlet, or any other device into an electrical box, a cordless drill can be used to quickly and efficiently screw the device into place.

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Power delivered to the runner is approximately 2.34 MW and the hydraulic efficiency of the Pelton wheel is approximately 88%.

Step-by-step explanation:

Calculate the coefficient of bucket using the bucket deflection angle:

cos(170°/2) = cos(85°) = 0.087

coefficient of bucket = 1 - 0.087 = 0.913

Calculate the mass flow rate:

mass flow rate = density x volumetric flow rate

= 1000 kg/m3 x 1 m3/s

= 1000 kg/s

Calculate the power delivered to the runner:

Power = mass flow rate x acceleration due to gravity x head x efficiency

= 1000 kg/s x 9.81 m/s2 x 270 m x 0.98 x 0.913

= 2341596.6 W

≈ 2.34 MW

Calculate the hydraulic efficiency:

Hydraulic efficiency = power output / power input

= 2.34 MW / (1000 kg/s x 9.81 m/s2 x 270 m x 0.98)

≈ 0.88 or 88%

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Answer:

Type C and D  DTCS.

The rocket's velocity is given by v = 299800 * sqrt(1/(1 + 4000/x)) km/s when measured in terms of the earth's surface.

A rocket must travel at least 7.9 kilometers per second (4.9 miles per second) in order to reach space if it is launched from the surface of the Earth. The orbital velocity, which is 7.9 km/s and more than 20 times the speed of sound, is measured in this manner.

Energy input minus energy output.

The rocket's launch energy is:

Ei equals (1/2) of kinetic energy plus potential energy.

mv02 - GMem/R, where ME is the mass of the Earth, G is the gravitational constant, and m is the mass of the rocket.

At a distance x from the earth's surface, the rocket's total energy is:

Ef is equal to the sum of the kinetic and potential energy, which is equal to (1/2)mv2 - GMem/(R + x), where v is the rocket's speed at x distance.

Energy is conserved since there is no air resistance, so:

Ei = Ef\s(1/2)

(1/2)mv02 - GMem/R = mv02 - GMem/(R + x)

By condensing and figuring out v, we arrive at:

sqrt(2GM/R) * sqrt(1/(R/x + 1)) gives v.

Simplifying and substituting R = 4,000 miles results in:

V is equal to sqrt(8.98 x 1010 m3/s2). * sqrt(1/(1 + 4000/x)) m/s\s= 299800

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The maximum allowable power for the silicon chip when it is flush mounted in a substrate with an unheated starting length of 20 mm is 0.136 W.

To find the maximum allowable power for the silicon chip, we need to use the equation for heat transfer from a flat plate in parallel flow:

q'' = h(Ts - T∞)

Where q'' is the heat flux, h is the heat transfer coefficient, Ts is the surface temperature, and T∞ is the free stream temperature.

We can rearrange this equation to find the maximum allowable power:

q'' = h(Ts - T∞)Pmax = q''A = hA(Ts - T∞)

Where Pmax is the maximum allowable power and A is the area of the chip. We are given the values for u∞, T∞, Ts, and A, so we can plug these into the equation to find Pmax:

u∞ = 20 m/s

T∞ = 24°C

Ts = 80°CA

= (10 mm × 10 mm)

= 0.0001 m²

We also need to find the value for h, which we can do using the equation for the Nusselt number for a flat plate in parallel flow:

[tex]NuL = 0.664Re^{0.5}Pr^0.33[/tex]

Where NuL is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. We can rearrange this equation to find h:

h = (NuLk)/where k is the thermal conductivity and L is the length of the chip. We can find the values for Re and Pr using the equations:

Re = (u∞L)/νPr = (Cpμ)/k

Where ν is the kinematic viscosity, Cp is the specific heat capacity, and μ is the dynamic viscosity. We can find the values for these properties using the given values for u∞ and T∞ and looking up the properties of air at these conditions:

ν = 15.68 × 10^-6 m²/s

Cp = 1007 J/kg·Kμ

= 18.46 × 10^-6 kg/m·sk

= 0.02624 W/m·K

We can now plug these values into the equations to find Re, Pr, NuL, and h:

Re = (20 m/s × 0.01 m)/(15.68 × 10^-6 m²/s)

= 12755.1Pr =

(1007 J/kg·K × 18.46 × 10^-6 kg/m·s)/(0.02624 W/m·K)

= 0.708NuL

= 0.664(12755.1^0.5)(0.708^0.33)

= 59.58h

= (59.58 × 0.02624 W/m·K)/0.01 m

= 155.6 W/m²

We can now plug these values into the equation for Pmax to find the maximum allowable power:

Pmax = (155.6 W/m²·K)(0.0001 m²)(80°C - 24°C) = 0.874 W

We can use the equation for the Nusselt number for a flat plate with an unheated starting length:

NuL = 0.3387(ReLPr)^(1/3)

Where L is the length of the heated portion of the plate.

We can plug in the values for Re, Pr, and L to find NuL:

NuL = 0.3387(12755.1 × 0.01 m × 0.708)^(1/3)

= 9.23

We can now use this value for NuL to find a new value for h:

h = (9.23 × 0.02624 W/m·K)/0.01 m = 24.25 W/m²·

We can now plug this value for h into the equation for Pmax to find the maximum allowable power:

Pmax = (24.25 W/m²·K)(0.0001 m²)(80°C - 24°C)

= 0.136 W

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All Fluorescent Lights and Tubes Should Be Recycled or Disposed as Hazardous Waste. In California, when fluorescent lights and tubes are thrown away because they contain mercury.

Yet, the Resource Conservation and Recovery Act classifies the minuscule amounts of highly dangerous mercury present in these fluorescent bulbs, as well as high-intensity discharge (HID) lamps and neon light bulbs, as hazardous waste (RCRA).

Due of the materials they contain, used light bulbs and lamps may be considered hazardous waste. Due to the mercury presence in them, fluorescent lamps are frequently hazardous waste, and lead solder used in LED light bulbs could make them hazardous garbage as well.

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Answer: The optical microscope, also referred to as a light microscope, is a type of microscope that commonly uses visible light and a system of lenses to generate magnified images of small objects. Optical microscopes are the oldest design of microscope and were possibly invented in their present compound form in the 17th century. Basic optical microscopes can be very simple, although many complex designs aim to improve resolution and sample contrast.

The object is placed on a stage and may be directly viewed through one or two eyepieces on the microscope. In high-power microscopes, both eyepieces typically show the same image, but with a stereo microscope, slightly different images are used to create a 3-D effect. A camera is typically used to capture the image (micrograph).

The sample can be lit in a variety of ways. Transparent objects can be lit from below and solid objects can be lit with light coming through (bright field) or around (dark field) the objective lens. Polarised light may be used to determine crystal orientation of metallic objects. Phase-contrast imaging can be used to increase image contrast by highlighting small details of differing refractive index.

A range of objective lenses with different magnification are usually provided mounted on a turret, allowing them to be rotated into place and providing an ability to zoom-in. The maximum magnification power of optical microscopes is typically limited to around 1000x because of the limited resolving power of visible light. While larger magnifications are possible no additional details of the object are resolved.

Alternatives to optical microscopy which do not use visible light include scanning electron microscopy and transmission electron microscopy and scanning probe microscopy and as a result, can achieve much greater magnifications.

Answer:

  see bold numbers below

Explanation:

Given the attached series-parallel circuit, you want to know ...

The circuit impedance is the sum of the series resistance and the parallel combination of the 1Ω resistor and the 3 mH inductor. For ω = 333, the inductor's impedance is Xl = jωL = j(333)(.003)Ω = j0.999Ω.

The total impedance is the sum ...

  Ztot = 10 + 1/(1/1 +1/j0.999) = 10.51∠2.73°

The total current in the circuit is ...

  Is = Vs/Ztot = 10∠45°/10.51∠2.73° = 0.9513∠42.27°

The branch currents are in reverse proportion to the branch impedance

  Ir = Is(Xl/(1+Xl)) = 0.6724∠87.30°

  Il = Is(1/(1+Xl)) = 0.6730∠-2.70°

Expressed as a sine function, these have the magnitude and phase angle indicated by the phasor:

  Is(t) = 0.9513·sin(333t +42.27°)

  Ir(t) = 0.6724·sin(333t +87.30°)

  Il(t) = 0.6730·sin(333t -2.70°)

At t=0, each of these current values is the magnitude of the current multiplied by the sine of the phase angle. In effect, it is the imaginary part of the current when it is expressed in complex form.

  Is(0) = 0.9513·sin(42.27°) = 0.6399 A

  Ir(0) = 0.6724·sin(87.30°) = 0.6716 A

  Il(0) = 0.6730·sin(-2.70°) = -.0317 A

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Additional comment

Solving these problems is immensely aided by a calculator that easily handles complex numbers. The one shown in the attachments does not thread polar conversions over a list, but otherwise works nicely for this problem. Angle mode is set to degrees. The value of x is 0.999i.