Problem 3. Consider the Cartesian (x, y, z) and spherical (r, 0, 0) coordinate systems shown below. We can see
that:
The unit vectors are related by:
er
eg
eo
Or, they can be inverted to obtain:
=
=
=
T
x
=
= r sin cos
Y
r sin
z = r cose
x, ex
ex =
sin cos de, + cos
ey
sin sin pe, + cos
ez = cose, sin eg
Show that the gradient of a scalar, a, is give by:
да
Ər
√x² + y² + 2²
sin
cos pe
+ sin
cos cos pe
+ cos
- sin de + cos de
Va er
+
1 да
r 20
z, e₂
Ф
sin o
Ө
eo +
sin pey + cos lez
sin pey - sinfez
cos peg - sin de
sin pee + cos de
1
r sin
r, e,
ed
да
do
-eo
y, eyn

Chemical manufacturers must present Product Identifier, Contact Information for the manufacturer and Hazard pictograms on the product's label.

A product label means a display of written, printed or graphic material that is printed on or affixed to a product or its immediate container.

Let's consider which of the following information must be presented on the product's label by chemical manufacturers.

Chemical manufacturers must present Product Identifier, Contact Information for the manufacturer and Hazard pictograms on the product's label.

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The majority of Precambrian rocks are fossil-free, which renders rock correlation difficult. Therefore, choice A is right.

The Precambrian rock is nearly 4.6 billion years old. The Precambrian is a geological time. Even though these rocks are found all over the world, they are predominantly found in the United States. Hot magma plumes from the earth's mantle were responsible for the formation of these rocks.

Rocks from the Precambrian period lack fossils. Before the multicellular organism commenced their life on this earth, these rocks were deposited. Macroalgae and microbial mats are among them. Stromatolites are one of the few Precambrian fossils that have been discovered.

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Answer:

d. To Murrow, Hitler was a threat to all of civilization

Explanation:

For Murrow, Hitler's rise was a serious problem and a major threat to the entire civilization. For this reason, he believed that covering news about Hitler's advance and the battles of Nazi Germany was essential, even if the American population did not see Hitler as a threat and the European population, believed that these reprotations were only a way to denigrate the image of the continent to the world.

For Murrow reporting on Hitler's actions was as important as reporting on natural disasters.

The looping function in C that performs an action first and then checks whether the action should continue to happen is do-while.

The do-while loop is a variation of the while loop. The loop executes once before testing the conditional statement because the block of statements inside the loop is executed once before testing the conditional statement. The loop continues to execute until the conditional statement is true.

The syntax for the do-while loop in C is as follows:

do{ statement1; statement2; . . .statementn;} while (condition);

The statements in the do-while loop's body are executed once before the conditional statement is checked. If the conditional statement is true, the loop will repeat until it is false. Because of the do-while loop's peculiarities, it is known as a post-tested loop.

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Answer:

or is the strongest evenger she hulk

Explanation:

?????????

Answer:

Thor!

Explanation:

In Thor: Ragnarok he beat the Hulk in order for Hulk to win thor had to be electrocuted and in Avengers: Endgame Thor is seen holding open the  "Floodgates" and withstanding the radiation from a dying star, also the fact that Thor is a god means that he is all powerful and the rightful heir to the throne to Asgard, plus the fact that he has defeated Loki multiple times a feat that not even the Hulk has done.

Answer:

The equilibrium temperature is 109.7°C

The total entropy change for the process is 0.23 kJ/K

Explanation:

The parameters given are;

The initial temperature of aluminium, T₁ₐ = 140°C = 413.15 K

Mass, m₁, of aluminium block = 28 kg

The specific heat of aluminium, c₁, at 400 K = 0.949 kJ/(kg·K)

The initial temperature of iron, T₁ₙ = 60°C = 333.15 K

Mass, m₂, of iron block = 36 kg

The specific heat of iron, c₂, at room temperature = 0.45 kJ/(kg·K)

The heat lost by the aluminium = Heat gained by the iron

The heat lost by the aluminium = m₁ × c₁ × (T₁ₐ - Tₓ)

The heat lost by the aluminium = 28 × 0.949 × (413.15 - Tₓ)

The heat gained by the iron =  m₂ × c₂ × (Tₓ - T₁ₙ)

The heat gained by the iron =  36 × 0.45 × (Tₓ - 333.15)

Hence;

28 × 0.949 × (413.15 - Tₓ) = 36 × 0.45 × (Tₓ - 333.15)

26.572 × (413.15 - Tₓ) = 16.2 × (Tₓ - 333.15)

∴ (26.572 + 16.2) × Tₓ = 26.572 × 413.15 + 16.2 × 333.15

42.772·Tₓ = 16375.2518

Tₓ = 382.85 K = 109.7°C

The total entropy change of the process is given by the following relation;

\(\Delta S = \Delta S_{Fe} + \Delta S_{Al}\)

\(=m_{1}c_{1}ln\dfrac{T_{x}}{T_{1n}}+m_{2}c_{2}ln\dfrac{T_{x}}{T_{1a}}\)

\(=28 \times 0.949 \times ln\dfrac{382.85}{413.15}+36 \times 0.45 \times ln\dfrac{382.85}{333.15} = 0.23 \, \dfrac{kJ}{K}\)

The option that is not a derived units is known to be option  E) kg.

The units that are known to be used for any form of derived quantities are said to be called the derived units.

They are:

Note that this unit are derived because they are known to be derived because they have to be solved for using different ways. The others such as kg m-3 is one that need to be derived to arrive at it.

Therefore, based on the above, one can say that The option that is not a derived units is known to be option  E) kg because it is one that cannot be derived,

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The following are derived units EXCEPT

Options

A) kg m-3

B)N

C)Ns

D)m3

E)kg

Explanation:

The earliest civil engineer known by name is Imhotep. As one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser (the Step Pyramid) at Saqqara in Egypt around 2630–2611 BC.

Answer:

See explanation.

Explanation:

Since no figure was given I solved a problem that was similar to the one you described that I worked in my mechanics of materials class. The method should be very similar for your figure. See attached image for my work.

If it is subjected to the couple determine the maximum shear stress in regions AC and CB of the shaft. G st = 75 GPa. Than the answer will be 52Mpa.

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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Answer:

The condition in which a problem exists

Explanation:

Context is the situation surrounding information, e.g. if you don't understand a word in a passge you can look for "context clues" where you use surrounding words to infer the meaning of the unknown one

The probability calculations for the given scenarios can be performed using the normal distribution with a mean of 1200 and a standard deviation of 80.

To calculate the probabilities, we can use the standard normal distribution table or statistical software such as R or Python.

a. To find the probability of a selected engine having a capacity greater than 1260, we calculate the z-score as (1260 - 1200) / 80 = 0.75. Using the z-score table or software, we find the probability associated with a z-score of 0.75.

b. For the probability of a selected engine having a capacity greater than 950, we calculate the z-score as (950 - 1200) / 80 = -3.125. Again, using the z-score table or software, we find the probability associated with a z-score of -3.125.

c. To determine the probability of a capacity of 1240 or less, we calculate the z-score for 1240 as (1240 - 1200) / 80 = 0.5. We find the probability associated with a z-score of 0.5.

d. The probability of a selected engine having a capacity less than 1130 can be calculated by finding the z-score for 1130 as (1130 - 1200) / 80 = -0.875. We find the probability associated with a z-score of -0.875.

e. For the probability of a capacity between 1100 and 1150, we calculate the z-scores for both values as (1100 - 1200) / 80 = -1.25 and (1150 - 1200) / 80 = -0.625. Then, we find the probabilities associated with these z-scores and calculate the difference between them to obtain the desired probability.

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Answer:

degree of saturation at optimummoisture content is 78.1 %.

Explanation:

The maximum dry unit weight of the soilYa is 16.8kN/mThe optimum moisture content of the soilwis 17 %.The specific gravity of soil G is 2.73.Calculation:Determine the degree of saturation (S)using the relation.Yd = Gs Yw/ 1+Gsw/sHere, Yw is the unit weight of water.Substitute 16.8 kN/m' for a, 2.73 for G,9.81 kN/m' for u, and 17 % for w.16.8= 2.73x9.811/2.73x1 .4641 26.78S-1.594S =-0.4641-0.594S= -0.4641S= 0.4641S = 0.781x 100S = 78.1 %16.80.594Therefore, the degree of saturation atoptimum moisture content is 78.1 %.

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

Explanation:

This is the case because installing electrical systems in a new construction does not involve spending time identifying problems in the electrical wiring, but an electrician maintaining electrical equipment in an existing structure first needs to;

Answer:

After construction ends, electrical wiring is harder to access.

Explanation:

The Curriculum Vitae (CV) for the foreman position should include Grade 12 School Certificate, relevant engineering certification, work experience, and EIZ membership.

Curriculum Vitae (CV) for the position of a qualified foreman at Kobils Engineering Company:

Personal Information: Include your full name, contact details (phone number, email address, residential address), and date of birth.

State your career objective as a qualified foreman, highlighting your commitment to overseeing operations efficiently and effectively.

Grade 12 School Certificate with five "O" levels.

Advanced Certificate in a relevant engineering field. Specify the specific engineering field and the institution where you obtained the certificate.

Provide details of your work experience, emphasizing relevant roles where you demonstrated leadership, problem-solving, and organizational skills. Include the company name, job title, duration of employment, and key responsibilities.

Minimum of two years of working experience should be mentioned.

Mention your membership in the Engineering Institute of Zambia (EIZ) as it demonstrates your commitment to professional development and adherence to industry standards.

Highlight your technical skills and knowledge relevant to the foreman role, such as project management, team coordination, quality control, and adherence to safety regulations.

Include any notable achievements or awards related to your engineering career, such as successful project completions or improvements in operational efficiency.

Provide the names, designations, contact details, and professional relationships of individuals who can provide references attesting to your qualifications and work ethic.

Remember to format the CV professionally, include accurate and up-to-date information, and tailor it to showcase your qualifications and experience specifically for the foreman position at Kobils Engineering Company.

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Boiler shell: It is the outermost part of the boiler, which contains the water and steam.Burner: It is a device used to burn the fuel (such as natural gas, oil, or coal) to generate heat.

Heat exchanger: It is a device used to transfer heat from the burner to the water, which is converted into steam or hot water.Water level gauge: It is a device used to indicate the level of water in the boiler.Pressure gauge: It is a device used to indicate the pressure inside the boiler.Safety valve: It is a device used to relieve the pressure inside the boiler if it exceeds the set limit.Control system: It is a system used to control the operation of the boiler, such as temperature, pressure, and fuel flow.Water treatment system: It is a system used to treat the water to prevent corrosion, scaling, and other problems.

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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;

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;

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

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;

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

At the minimum value, we have;

Which gives;

16·π·r³ = 6·V

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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The correlation between acid rain and human population density in Russia is a complex issue that requires careful analysis and consideration of various factors.

Acid rain is caused by emissions of sulfur dioxide and nitrogen oxides, primarily from industrial activities and fossil fuel combustion. These pollutants can be transported over long distances by air currents and eventually deposited as acid rain.

When examining the correlation with human population density in Russia, several factors come into play. Areas with high population density tend to have more industrial and urban activities, which can contribute to higher emissions of pollutants. In densely populated regions with significant industrial activity, the likelihood of acid rain occurrence may increase.

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It is uncommon for electrocution to cause crane incidents: False.

Electrocution can be defined as a process through which a certain amount of electric current (electricity) passes through the body of a living organism, thereby, leading to death or severe injury.

According to the occupational safety and health administration (OSHA), it is very common for electrocution to cause crane incidents and accidents when adequate safety precautions are not adopted.

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Answer: Why is even here then.

Explanation:

Answer:

The correct answer is "Building automation system (BAS)".

A Building Automation System (BAS) is responsible for maximizing building efficiency by managing all of a building's electrical and mechanical operations. BAS uses a network of sensors, controllers, and software to monitor and control various building systems, including heating, ventilation, air conditioning, lighting, and security.

BAS is designed to optimize building performance by automating routine tasks, responding to changing conditions, and identifying and addressing problems before they become critical. By providing real-time data and analytics, BAS allows building managers to make informed decisions about energy usage, equipment maintenance, and system upgrades.

Overall, BAS helps building owners and managers to reduce energy consumption, lower operating costs, and improve occupant comfort and safety. It is an essential component of modern building design and management, and plays a critical role in achieving sustainable and efficient building operations.

When the blower control is set on "HIGH" the blower motor receives full

battery voltage through a high-speed resistor.

A resistor is a device that provides electrical resistance in a circuit. A

device contains different resistors which regulates the amount of current

flowing through it.

This permits the regulation of the blower which have various speed ranges

available. The high-speed resistor is responsible for receiving the voltage

in a blower when the control is  set on "HIGH".

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Answer:

a) Db = 10.05 in

b) The operation is not feasible

Explanation:

Let's begin by listing out the given variables:

Thickness = 1/8 in, Height (h) = 3.8 in,

Diameter (Dp) = 5 in ⇒ rp = Dp ÷ 2 = 5 ÷ 2 = 2.5 in

a) Area of cup = Area of wall + Area of base

A = 2πh(rp) + π(rp)²

A = (2π * 2.5 * 3.8) + (π * 2.5²)

A = 59.69 + 19.635 = 79.325 in²

A ≈ 79.33 in²

But π(rb)² = 79.33 ⇒ rb² = 79.33 ÷ π

rb² = 25.25

rb = 5.025 ⇒ Db = 2 * rb = 2 * 5.025 = 10.05 in

Db = 10.05 in

b) To calculate for feasibility, we use the formula, draw ratio equals diameter of the blank divided by diameter of the punch

Mathematically,

DR = Db ÷ Dp

DR = 10.05 ÷ 5 = 2.01

DR = 2.01

DR > 2 ⇒ the operation is not feasible

For an operation to be feasible, it must have a drawing ratio limit of 2 or lesser

Answer:

Past tense of hear = heard

The initial volume of the cylinder was 2.54 m³

Apply the ideal gas law formula as below,

PV = nRT

Here P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

For the reversible, the ammonia undergoes an isentropic (i.e., constant entropy) process. This means that the entropy change of the ammonia is zero, and we can use the following equation to relate the initial and final states:

\(\dfrac{T_1}{T_2} = \dfrac{(P_1}{P_2})^{(\frac{(\gamma-1)}{\gamma}\)

The given temperatures are,

T₁ = 60 + 273 = 333 K

T₂ = -20 + 273 = 253 K

From the ideal gas equation,

PV = nRT

\(n = \dfrac{PV}{RT_1} \\n = \dfrac{(1200 )}{(V)}\times\dfrac{8314 }{333 }\\\)

n = 0.0567 V (in kmol)

Use the given work to find the change in the internal energy of the ammonia:

ΔU = Q - W = 0 - (-200 kJ) = 200 kJ

Since the process is reversible and isentropic, the change in internal energy is given by:

ΔU = nCv(T₂ - T₁) = nR/(γ-1)(T₂ - T₁)

where Cv is the specific heat at constant volume (which is approximately 0.75 kJ/(kg*K) for ammonia).

Substituting the known values and solving for V, we get:

\(V = \dfrac{\Delta{U}}{((\gamma-1)nCv))}\times \dfrac{T_1}{T_2} \\V= \dfrac{200} {((1.4-1)(0.0567 )(0.75)}\times \dfrac{333} {253}\)

V = 2.54 m³

Therefore, the initial volume of the cylinder was 2.54 m³.

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