Q-2 Two shafts, A and B, are co-axial (aligned along x-axis). Gear-C is rigidly mounted on shaft-A and turn together. Compound gears D-E, carried with an arm-B, rotate together on the same pin. Gear-D meshes with the sun-gear-C and gear-E with the internal gear-G (fixed), where its axis is concentric with the axis of shaft-A
a) Referring to the figures below determine the number of teeth NG on internal gear G assuming that all gears have the same module, m = 5 mm. [12 pts.]
b) If shaft A rotates at 530 rev/min. (c.w.) determine the magnitude and direction of the speed of shaft B, and that of compound gears D and E. [28 pts.]
[Given: NC = N2= 50-T, ND = N3 = 20-T, NE = = N4 = 35-T. NG =N5 = ?, and nC = nA = n2 = 530 rpm. (c.w.)]

The magnitude of FB is 700 N, and its orientation is 59.5° from the x-axis.

Since the resultant force is directed along the positive y-axis, we know that the y-component of FB must be equal and opposite to the y-component of Fa, which is 700 N * sin(30°) = 350 N. Therefore, the magnitude of the y-component of FB is also 350 N.

To find the magnitude of FB itself, we can use the Pythagorean theorem:

[tex]FB^2 = (y-component of FB)^2 + (x-component of FB)^2[/tex]

[tex]FB^2 = (350 N)^2 + (FBx)^2[/tex]

We do not have enough information to directly solve for FBx, but we can use the fact that the angle between FB and the x-axis is the complement of the angle between Fa and the x-axis (since the two forces are perpendicular). Therefore,

tan(θ) = FBx / 350 N

where θ is the angle between FB and the x-axis.

We also know that the magnitude of FB is equal to the magnitude of Fa, which is 700 N. Therefore, we have:

[tex]FB^2 = FBx^2 + (350 N)^2 = (700 N)^2[/tex]

Solving for FBx, we get:

[tex]FBx = sqrt((700 N)^2 - (350 N)^2) = 606 N[/tex]

Using the equation for tan(θ), we get:

θ = arctan(FBx / 350 N) = 59.5°

Therefore, the magnitude of FB is 700 N, and its orientation is 59.5° from the x-axis.

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(a) The augmented matrix whose row reduction would solve the system is:

$$\left[\begin{array}{ccc|c} 1 & 2 & -1 & 5 \\ 2 & -1 & 1 & 2 \\ 3 & 1 & -2 & 8 \end{array}\right]$$

(b) The vector combination equivalent to the system is:

$$x\begin{pmatrix}1\\2\\3\end{pmatrix}+y\begin{pmatrix}2\\-1\\1\end{pmatrix}+z\begin{pmatrix}-1\\1\\-2\end{pmatrix}=\begin{pmatrix}5\\2\\8\end{pmatrix}$$ (c) The matrix equation equivalent to the system is:$$\begin{pmatrix}1 & 2 & -1 \\ 2 & -1 & 1 \\ 3 & 1 & -2 \end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}5\\2\\8\end{pmatrix}$$

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The magnitude of the magnetic flux density B at a point on the surface of the earth directly below the power line is approximately 1.27 x 10⁻⁴ T.

The magnitude of the magnetic flux density B can be calculated using the Ampere's Law, which relates the magnetic field around a current-carrying wire to the current flowing through it. The formula for Ampere's Law is:

B = μ₀I / 2πr

Where B is the magnetic flux density in tesla (T), μ₀ is the permeability of free space (4π x 10⁻⁷ Tm/A), I is the current in amperes (A), and r is the distance from the wire in meters (m).

In this case, the current I is 1000 A, and the distance r is the height of the power line above the earth, which is 50 m. Plugging these values into the formula, we get:

B = (4π x 10⁻⁷ Tm/A)(1000 A) / (2π)(50 m)

B = (4 x 10⁻⁷ Tm)(1000) / (100π m)

B = 4 x 10⁻⁴ T / π

B ≈ 1.27 x 10⁻⁴ T

Therefore, the magnitude of the magnetic flux density B at a point on the surface of the earth directly below the power line is approximately 1.27 x 10⁻⁴ T.

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The total error is 13.36, which is acceptable if it is within the allowable error range for the project.

To calculate the elevation for stations along an irrigation canal, we need to use the following formula:

Elevation of Station = Elevation of BM1 + Backsight - Foresight

First, we need to find the backsight and foresight for each station. The backsight is the reading taken on the benchmark or turning point, while the foresight is the reading taken on the intermediate point.

Station | Backsight | Foresight | Elevation
---         | ---             | ---            | ---
BM1     | -                | -              | 646.52
1          | 1.35           | 0.98        | 646.89
2          | 1.22           | 1.10        | 647.01
3          | 1.15           | 0.95        | 647.21
4          | 1.18           | 1.02        | 647.37
5          | 1.25           | 1.08        | 647.54
BM2     | 1.32          | -              | 659.88

Now, we can calculate the elevation for each station using the formula:

Elevation of Station 1 = 646.52 + 1.35 - 0.98 = 646.89
Elevation of Station 2 = 646.89 + 1.22 - 1.10 = 647.01
Elevation of Station 3 = 647.01 + 1.15 - 0.95 = 647.21
Elevation of Station 4 = 647.21 + 1.18 - 1.02 = 647.37
Elevation of Station 5 = 647.37 + 1.25 - 1.08 = 647.54

Finally, we can calculate the total error by subtracting the elevation of BM1 from the elevation of BM2:

Total Error = Elevation of BM2 - Elevation of BM1 = 659.88 - 646.52 = 13.36

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The quicksort algorithm starts by taking the first value, 6, as the pivot. We then split the array into two parts, one with values smaller than 6, and one with values larger than 6. After the first split, the array looks like this:

[3, 1, 5, 4, 2], [8, 7]

Traversing the smaller values first, we split the first sub-array again into two parts, one with values smaller than 3, and one with values larger than 3. After the second split, the array looks like this:

[1, 2], [3], [5, 4], [8, 7]

We split the sub-array containing 1 and 2 again into two parts, one with values smaller than 1, and one with values larger than 1. After the third split, the array looks like this:

[], [1], [2], [3], [5, 4], [8, 7]

We have now reached the point where all sub-arrays contain either one value or zero values, so the array is now sorted and looks like this:

[], [1], [2], [3], [4], [5], [7], [8]

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Needle nose pliers are best used for option C, shaping wires. Needle nose pliers have a long, pointed and narrow tip that allows them to grip and manipulate wires in tight spaces or with precision.

What is the use of Needle nose pliers?

Needle nose pliers are a versatile tool used for gripping, bending, shaping and cutting wires, as well as for holding small objects in hard-to-reach places. They have a long, narrow and pointed tip that allows for precise handling of small parts or wires in tight spaces.

For example, they can be used by electricians to bend and shape wires, make connections or install small components in a circuit board. They are also useful for jewelry making, crafting, and other fine tasks that require precision and dexterity.

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Answer: Your welcome!

Explanation:

There are three unknowns in a FBD of the beam: the reaction force at point A, the reaction force at point B, and the shear force at point C. The reaction forces at points A and B indicate the forces exerted by the beam on the cable and pulley at each end. The shear force at point C indicates the force exerted by the load on the beam.

The free-body diagram of the beam which supports the 80-kg load and is supported by the pin at A .

The first image shows the diagram of the beam and the second image shows the free-body diagram of the beam.

The resolution of forces in the system is well understood by the principle of equilibrium where a stationary body will remain balanced when subject to parallel forces provided that the total sum of the overall external forces is zero.

The free-body diagram is a graphical representation used to visualize the forces applied to an object.

Therefore, we can conclude that the free-body diagram of the beam which supports the 80-kg load and is supported by the pin at A.

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The output of the first code snippet is "12345".

This is because the switch statement does not have any break statements, so it will continue executing each case until it reaches the default case.

The do...while loop will iterate 3 times. This is because the loop will execute the statements inside the loop until the condition (num <= 3) is no longer true. Since num starts at 1 and is incremented by 1 each time the loop executes, the loop will iterate 3 times before the condition is no longer true.

The value of x after the statement "x /= y;" executes is 1. This is because the /= operator is equivalent to "x = x / y", so x will be assigned the value of x divided by y, which is 3 divided by 2, or 1.

The correct way to rewrite the code as an if-else statement is:

if(temp <= 32){
 System.out.printf("freezing");
} else {
 System.out.printf("above freezing");
}

This is because the original code uses a ternary operator, which is a shorthand way of writing an if-else statement. The ternary operator checks the condition (temp <= 32), and if it is true, it executes the first statement ("freezing"), otherwise it executes the second statement ("above freezing"). The rewritten code does the same thing using an if-else statement.

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The equivalent resultant force is 3200 lb and its location is 12.56 ft from point O.

To find the equivalent resultant force and its location, we need to use the principle of equilibrium. The sum of the moments about point O should be equal to zero.

First, let's calculate the resultant force of the distributed load.

Resultant force = (100 lb/ft)(8 ft) + (300 lb/ft)(9 ft) + 50 lb = 3200 lb

Now, let's find the location of the resultant force by taking the moment about point O.

ΣMO = 0 = (100 lb/ft)(8 ft)(4 ft) + (300 lb/ft)(9 ft)(8 + 4.5 ft) + (50 lb)(17 ft) - (3200 lb)(x)

Solving for x, we get:

x = 12.56 ft

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To evaluate the given mathematical expressions and assign the result to the indicated variable name, we can use the following MATLAB commands:

For the first expression:
```
Answer1 = 15.5*log10(1234.56-8.53*1)*5.23+3.7*cos(4.2+(4.2+1));
```

For the second expression:
```
Answer1 = 10e-3/5-3/5*(cos(35)+3*sin(5));
```

For the third expression:
```
Answer1 = cos(35*pi/180)-sec(35*pi/180)^2/tan(70*pi/180);
```

Note that we have used the `pi/180` conversion factor to convert the angles from degrees to radians, since MATLAB works with radians by default. Also, we have used the `^` operator to indicate exponentiation, and the `*` operator to indicate multiplication.

After executing these commands, the variable `Answer1` will contain the result of the corresponding expression, and we can use it for further calculations or display it using the `disp` function:

```
disp(Answer1);
```

This will show the result of the expression on the MATLAB command window.

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The maximum acceleration of the triangular-shaped cart so that the box does not slide on the cart can be calculated using the formula for static friction. The formula for static friction is Fs = μsN, where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.

In this case, the normal force is equal to the weight of the box, which is mg, where m is the mass of the box and g is the acceleration due to gravity. The force of static friction is also equal to the mass of the box times the acceleration of the cart, or ma.

So we can set up the equation Fs = ma = μsN = μsmg. Rearranging the equation to solve for the acceleration of the cart, we get a = μsg.

Since the angle theta is given, we can use the trigonometric function sine to find the coefficient of static friction. The sine of an angle is equal to the opposite side divided by the hypotenuse, so sin(theta) = μs.

Substituting this back into the equation for the acceleration of the cart, we get a = (sin(theta))g.

Therefore, the maximum acceleration of the triangular-shaped cart so that the box does not slide on the cart is a = (sin(theta))g.

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Always refer to the NEC rules for the specific installation type and location to ensure code compliance. Hence,The correct answer is 8.

According to NEC Table 1, when installing a 3/8 -in. flexible metal conduit using inside fittings, the maximum number of 14 AWG THHN conductors, including an equipment grounding conductor, that can be installed is 8.

Note that this table applies only to THHN/THWN conductors with nylon coating and stranded copper. It does not take into account the quantity of neutral conductors or equipment grounding conductors that may be required for a given installation.

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Answer: D. Cylindrical

Explanation:

The use of a center line plus diameter symbol indicates that the part is Cylindrical

During test generation, it is not advisable to combine several test requirements to generate one test case when the test requirements are unrelated or contradictory. This can lead to confusion and inaccuracies in the test results.

For example, if one test requirement is to test the functionality of a login page and another test requirement is to test the functionality of a shopping cart, it would not be advisable to combine these two test requirements into one test case. This is because the login page and the shopping cart are unrelated and testing them together would not provide accurate results.

Another example is if one test requirement is to test the functionality of a search bar with a specific keyword and another test requirement is to test the functionality of the search bar without any keywords. These two test requirements are contradictory and combining them into one test case would not provide accurate results.

In conclusion, it is not advisable to combine several test requirements to generate one test case when the test requirements are unrelated or contradictory. This can lead to confusion and inaccuracies in the test results.

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The statements that are testable by accepted methods of science are:

- "Mars once had liquid water on its surface"
- "Bacteria acquire resistance to antibiotics through changes in their DNA"
- "Earth orbits the Sun every 365.25 days"
- "There will be a solar eclipse next Tuesday at 11 am"

The statements that are not testable by accepted methods of science are:

- "Hurricane Katrina was an act of God"
- "People born under the sign of Sagittarius are twice as likely to be teachers as anyone else"
- "Vince Young is the greatest quarterback of all time"

The testable statements can be investigated and proven or disproven through the use of accepted scientific methods, such as observation, experimentation, and data analysis. The non-testable statements, on the other hand, cannot be proven or disproven through these methods because they are based on subjective beliefs or opinions.

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A plastic deformation is defined as a change in shape of the part between the damaged and undamaged area that is smooth and continuous. When the part is straightened, it is returned to its proper shape and state without any areas of permanent deformation.

Plastic deformation is considered as a crucial concept in mechanical engineering and materials science because it influences material qualities such as the strength and durability. It is also crucial in manufacturing operations since it influences the quality of the items produced.

Plastic deformation may occur as a result of a number of operations, including bending, stretching, pressing, and forging.

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The shape, interior surface, and size of a port all determine its efficiency. The three types of valve seals are compression seals, O-ring seals, and PTFE seals.

Each type has its own advantages and disadvantages, and one may be more suitable for specific purposes than the others. O-ring seals - These seals are made of a rubber material and are commonly used in low-pressure applications. They provide a good seal and are relatively easy to install and replace. Lip seals - These seals are made of a rubber material and have a lip that contacts the valve stem or shaft. They are commonly used in applications that require high-pressure sealing, such as hydraulic systems. Mechanical seals - These seals use a combination of metal and rubber components to provide a tight seal. They are commonly used in applications that require high-pressure or high-temperature sealing, such as pumps and compressors.

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In many cases, there is a separate "control module" for the systems such as antil-ock brakes, supplemental restraint-systems and many of the engine controls.

What are control module?

Control modules are electronic devices that control and monitor specific systems in a vehicle, such as antilock brakes and engine controls. They receive input from sensors and use this information to make decisions and adjust the operation of the system they control.

These control modules are specialized electronic devices that are responsible for controlling and monitoring specific systems or functions within a vehicle.

They typically receive input from various sensors and use this information to make decisions and adjust the operation of the system they control. Control modules may communicate with other modules or with a central vehicle computer to coordinate overall vehicle operation.

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As there are 12 inches in a foot, 8 feet equals 96 inches, and 4 feet equals 48 inches. Thus, we may cut a single 8' by 4' piece of material into 12 pieces, each measuring 21 3/4" x 16".

A typical plywood sheet measuring 4 feet by 8 feet covers 32 square feet. If your roof is 1,600 square feet in size, you will need roughly 50 sheets to cover it if you divide 1,600 by 32.

Now that we know how many pieces of material (8'x4') measuring 21 3/4" by 16" we can get, we can :

By dividing the material's length by the length of each piece, we arrive at:

21.75 inches / 96 inches equals 4.41 (rounded to two decimal places)

By dividing the material's breadth by the width of each component, we arrive at:

48 inches / 16 inches equals 3.

As a result, we can fit 4 pieces along the material's length and 3 pieces along its width, for a total of: 4 x 3 = 12 pieces.

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To compute the critical stress required for the propagation of an internal crack of length 0.3 mm in aluminum oxide with a specific surface energy of 0.90 j/m2 and a modulus of elasticity of 393 GPa, we can use the following equation:

Critical Stress = (2 x Specific Surface Energy x Modulus of Elasticity) / Crack Length

Plugging in our values:

Critical Stress = (2 x 0.90 j/m2 x 393 GPa) / 0.3 mm

Critical Stress = 8,760 MPa

The specific surface energy for aluminum oxide is given as 0.90 J/m2 and its modulus of elasticity is 393 GPa. We are to compute the critical stress required for the propagation of an internal crack of length 0.3 mm.

Given formulae: Tensile Stress = F/A, where F is the tensile force applied and A is the cross-sectional area of the surface upon which the force is applied Modulus of Elasticity = Tensile Stress/Strain, where strain is the ratio of the change in length of an object to the original length.

Critical Stress = σ_0 √πa/2 * Y_b

The first step is to compute the tensile stress, which is given as:

Tensile Stress = F/A

We can find the cross-sectional area using the formula for the area of a circle. This formula is given as: Area = πr^2, where r is the radius of the circle. We can find the radius of the circle as r = 0.3/2 mm = 0.15 mm = 0.00015 m. We can now compute the area of the circle as follows: Area = π(0.00015)^2 = 7.07 × 10^-8 m^2.The tensile stress is given as: Tensile Stress = F/A = σ, where F is the tensile force applied, and A is the cross-sectional area of the surface upon which the force is applied. We can rearrange the equation above to get: F = Aσ = 7.07 × 10^-8 × σThe modulus of elasticity is given as:

Modulus of Elasticity = Tensile Stress/Strain, where strain is the ratio of the change in length of an object to the original length.

We can rearrange the equation above to get: Tensile Stress = Modulus of Elasticity × Strain

Let us assume that the original length of the object is L, and the change in length of the object is ΔL, then the strain is given as: Strain = ΔL/L

The critical stress is given as: Critical Stress = σ_0 √πa/2 * Y_b . We can now use the values of the specific surface energy and the modulus of elasticity to calculate the critical stress as follows: Critical Stress = √((2 × 0.90 × 10^-6 × 393 × 10^9)/((π × 0.3 × 10^-3)/2)) = 97.2 MPa

Therefore, the critical stress required for the propagation of an internal crack of length 0.3 mm is 97.2 MPa.

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Answer:

If a pedestrian walks when the sign says don't walk, you should stop and allow the pedestrian to cross the street.

Explanation:

Even if the pedestrian is advised to stop, the pedestrian has the right of way, and the driver will be penalized if the pedestrian is hit with any vehicle.

This is a transient problem because the temperature throughout the bar changes suddenly due to the introduction of an electric current and an airstream. The heat conduction equation for this problem can be written as:

∂T/∂t = k(∂^2T/∂x^2 + ∂^2T/∂y^2)

Since the width W is much greater than the thickness L, we can simplify the equation by assuming that the temperature distribution is one-dimensional in the y-direction. Therefore, the equation becomes:

∂T/∂t = k(∂^2T/∂y^2)

The boundary and initial conditions for this problem are as follows:

- At the bottom surface, the temperature is maintained at T0: T(y=0) = T0
- At the top surface, the temperature is affected by the airstream: -k(∂T/∂y)|y=L = h(T(infinity) - T(y=L))
- Initially, the temperature throughout the bar is equal to that of the sink: T(y,t=0) = T0

These conditions are necessary to solve the equation for the temperature distribution in the copper bar.

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The best place to adjust speed to steer through a curve is at the beginning of the curve.

This is because when entering the curve, it is important to be travelling at a speed that is appropriate for the radius of the curve. Entering the curve at a slower speed will give you more control over the vehicle and allow you to navigate the curve safely.

Speed should be gradually reduced before entering a curve, and the driver should maintain a steady speed throughout the curve. Braking while turning can be dangerous, as it can cause the vehicle to skid or lose control. It is also important to ensure that the vehicle is in the correct gear for the speed and road conditions.

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x + 2 * x is the correct option. The above-selected option demonstrates implicit conversion, which is an automated type of conversion. Thus, option B is correct.

The series of conversions are necessary to change the type of a function call's argument to that of the parameter with the same name in the function declaration is known as an implicit conversion sequence. For each parameter, the compiler tries to identify an implicit conversion sequence.

If both user-defined conversion sequences A and B contain the same user-defined conversion function or constructor, and if the second standard conversion sequence of A is superior to the second standard conversion sequence of B, then user-defined conversion sequence A is preferable to user-defined conversion sequence B.

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Where the above conditions are given the amount of money placed in the trust fund if guaranteed interest is 16% per year will be P 12,166,666.67.

To solve this problem, we need to use the formula for the future value of an annuity:

FV = PMT x [(1 + r)ⁿ⁻¹] / r

where:

FV = future value

PMT = payment per period (in this case, the earnings of P 400,000 every 4 years)

r = interest rate per period (in this case, 16% per year, or 4% per 4-year period)

n = number of periods (in this case, 20 years / 4 years per period = 5 periods)

Plugging in the numbers, we get:

FV = 400,000 x [(1 + 0.04)⁵⁻¹] / 0.04

FV = 400,000 x 1.2167 / 0.04

FV = 12,166,666.67

Therefore, the amount of money placed in the trust fund is P 12,166,666.67.

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The magnitude of the small gravitational force of mutual attraction is 1.67 x 10⁻⁷ N.

Gravitational force is the attractive force between two bodies in the universe due to their masses. It is the fundamental force of nature, and the most important force in the universe. It affects all matter from the smallest atom to planets, stars and galaxies.

The magnitude of the small gravitational force of mutual attraction can be calculated using the equation F = G × m1 × m² / r², where G is the universal gravitational constant (6.67 × 10^-11 N*m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between them. Therefore, the equation becomes F = G × m1² / r².

For this problem, m1 = m2 = 0.001 kg, r = 40 mm = 0.04 m.

Therefore, F = G × m1² / r² = 6.67 x 10⁻¹¹ N × m2/kg² * (0.001 kg)² / (0.04 m)² = 1.67 x 10⁻⁷ N.

Therefore, the magnitude of the small gravitational force of mutual attraction is 1.67 x 10⁻⁷ N.

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According to the given statement, technician A says that an intake manifold vacuum leak may cause a high idle speed. Technician B says that a dirty IAC bypass passage will not cause the idle speed to be below specifications.

We have to determine who is correct.According to the given statement, technician A is correct. An intake manifold vacuum leak will cause high idle speed. The vacuum leak disrupts the airflow signal that the Powertrain

Control Module (PCM) uses to regulate idle speed. Furthermore, vacuum leaks can cause excessive crankcase ventilation, which can cause fuel dilution and other issues. Technician B is incorrect. The IAC bypass passage regulates idle speed by diverting air around the throttle plate.

A dirty or clogged IAC bypass passage may disrupt the airflow that the PCM uses to regulate idle speed, causing it to be outside of specifications. Thus, we can conclude that only technician A is correct.

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During a drought, the water table typically drops due to reduced precipitation and increased evaporation.

The water table is the underground layer of soil or rock that is saturated with water, and it fluctuates based on various factors such as rainfall, surface water levels, and human activities such as groundwater pumping.

Drought conditions reduce the amount of water available to replenish the water table, which can lead to a depletion of groundwater resources.

This can have negative impacts on ecosystems, agriculture, and human communities that rely on groundwater for drinking water and other uses.

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Where the above conditions exists, the DC resistance at 50°C with skin effect is 77.2% higher than the DC resistance at 50°C without skin effect.

To calculate the DC resistance at 20°C, we can use the given dc resistance per 1000 ft:

DC resistance per ft = (0.01558 ohm / 1000 ft) * (1113 kcmil / 1000 cmil)

= 0.01735 ohm/ft

Next, we need to account for the 2% increase in resistance due to spiraling:

Resistance increase due to spiraling = 2% * 0.01735 ohm/ft

= 0.000347 ohm/ft

Therefore, the total DC resistance at 20°C is:

DC resistance at 20°C = 0.01735 ohm/ft + 0.000347 ohm/ft

= 0.017697 ohm/ft

To calculate the DC resistance at 50°C, we need to use the temperature coefficient of resistance for aluminum, which is 0.00403/°C. The resistance at 50°C can be found using the following formula:

R(50) = R(20) [1 + α(50 - 20)]

where R(20) is the DC resistance at 20°C and

α is the temperature coefficient of resistance for aluminum.

R(50) = 0.017697 ohm/ft [1 + 0.00403/°C * (50°C - 20°C)] = 0.019371 ohm/ft

The percentage increase due to skin effect can be calculated using the following formula:

% increase due to skin effect = 100 * (R(50) - R(dc)) / R(dc)

where R(dc) is the DC resistance at 50°C without skin effect.

R(dc) = 0.0956 ohm/mile * 5280 ft/mile / 61 strands

= 0.08503475442 ohm/ft

% increase due to skin effect = 100 * (0.019371 ohm/ft - 0.08503475442 ohm/ft) / 0.08503475442 ohm/ft

= 77.2%

Therefore, the DC resistance at 50°C with skin effect is 77.2% higher than the DC resistance at 50°C without skin effect.

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