The angle grinder disc is turned at speeds that range from 5000 to rpm.

The pressure of seawater will be 2.14*107 N/m2 and the density will be 8.53*103 kg/m3.

Pressure is a type of force applied to an object by another object over a surface area. Pressure is measured in units of force per unit area and is usually expressed in terms of pascals (Pa).

The bulk modulus of elasticity, K, is a measure of the stiffness of a material and is defined as the ratio of bulk stress to the resulting strain. In this problem, we need to calculate the density and pressure at a depth of 2500 m, based on the given bulk modulus and 98 kPa pressure at the surface.
To solve this problem, we will use the equation K = -dp/dρ, where dp is the change in pressure with depth and dρ is the change in density with depth. Since we are given the bulk modulus and pressure on the surface, we can calculate the change in density with depth as follows:
dρ = -K*dp/dz
where dp = rgdz and rg is the gravity of the Earth. Substituting these values, we get:
dρ = -2.34*109*98*103/(9.8*2500) = -7.78*103 kg/m3
This means that for every metre of depth, the density of seawater decreases by 7.78*103 kg/m3. Therefore, at a depth of 2500 m, the density of seawater will be:
ρ = 1030 - 7.78*103*2500 = 8.53*103 kg/m3
Similarly, we can calculate the pressure at a depth of 2500 m using the equation P = P0 + rgdz, where P0 is the pressure at the surface. Substituting the values, we get:
P = 98*103 + 9.8*2500*8.53*103 = 2.14*107 N/m2
Therefore, at a depth of 2500 m, the pressure of seawater will be 2.14*107 N/m2 and the density will be 8.53*103 kg/m3.

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The velocity of airplane will be 317.4 m/s.

The velocity of an airplane flying at a standard altitude of 5 km can be calculated using the stagnation pressure of the pitot tube mounted at the nose.

The stagnation pressure of the pitot tube was measured at 0.957 bar. Assuming the airplane is flying at high subsonic speed and flow is compressible, the velocity of the airplane can be calculated using the equation:

Velocity (v) = sqrt[2*(pstag-pamb)/ρ]

Where pstag is the stagnation pressure (0.957 bar), pamb is the ambient pressure (0.1013 bar at 5 km altitude), and ρ is the air density (1.225 kg/m3).

Plugging in the given values, the velocity of the airplane is 317.4 m/s.

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To observe the structure of Beauvais Cathedral's roof and the form of the flying buttresses that hold its vaults in place, you would consult a sectional drawing of architectural drawing.

What is architectural drawing?
Architectural drawing is a visual representation of a proposed or existing building or structure. It is used to communicate ideas and plans for the design of a project. The drawings are typically done by an architect, an architectural technician, or a draftsman. Architectural drawings are typically composed of multiple components, including floor plans, elevations, sections, details, and sometimes 3D renderings. They are used to illustrate how different parts of the building fit together, what materials will be used, and how the project will interact with its environment.

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The process of creating sugar from raw sugar cane involves several steps. First, the raw cane is passed through a series of crushers to extract the juice from the cane.

A crusher is a machine designed to reduce large rocks into smaller rocks, gravel, or rock dust.

This step also adds about 5% extra mass of water to the sugar cane to help with the extraction process. The crushed cane and liquid juice are then sent to a filter press, which creates a cake containing 4% of the weight of the cane juice. This cake has a composition similar to the overall non-fiber content of the raw cane. The filtrate is then sent to an evaporator, where enough water is evaporated to obtain a pale yellow juice that is 41% water. Finally, the liquid is crystallized to produce sugar crystals, which are typically about 99.8% sucrose.

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Answer: Droughts, pumping effects, and rainfall variations affect the groundwater level height.

Explanation: If a well is pumped at a faster rate than the aquifer around it is recharged by precipitation or other underground flow, then water levels in the well can be lowered.

A "While" Loop is used to repeatedly execute a particular block of code until a condition is met.

The responses to the questions are listed below. The operation that determines whether the condition x 10 is true is assessed first because the operator is used first. The reason for this is that we use the post increment operator for x. As a result, x is first used for the operation we are performing before being raised by 1. According to semantics, the variable's value is increased by 1 by both prefix and postfix ++. The result of the operator is the NEW/CURRENT value stored in the variable if the ++ is placed before the variable (a prefix operator); the result of the operator is the value stored in the variable if the ++ is written after the variable (a postfix operator).

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The 36,000 pound single axle load is twice as much as the 18,000 pound single axle load, so it is twice as much stress on the pavement.

What is axie load?
Axie Load is a decentralized application (dApp) that allows users to earn cryptocurrency rewards simply by playing games. The platform focuses on providing fun, engaging and rewarding experiences for both gamers and crypto owners. The games are designed to be easy to learn, but difficult to master, making them suitable for players of all skill levels. Axie Load also integrates with popular blockchain projects such as Ethereum, allowing users to store their rewards in their own wallets. With its unique combination of gaming and crypto rewards, Axie Load is an exciting platform for users looking to explore the world of blockchain gaming.

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Answer:

The thickness of the oil reservoir is 10cm, the production rate of oil is 100m3, the well radius is 10cm, the permeability of the reservoir is 1um2, the porosity is 0.2, the viscosity of the oil is 4mPa.s, the density of oil is 850kg/m3. If the flow regime can be considered as linear flow, can this flow in the reservoir satisfy Darcy's

The best device to help prevent moisture from collecting in raceway systems is integral drains.

Integral drains are specifically designed to allow water to drain away from the system without the need for additional components. Elbows and strainers are not effective for this purpose, and seal-off fittings are primarily used for dust and debris protection.

Raceway systems are a type of electrical wiring system used to protect electrical wires and cables. They are typically used in industrial applications and are designed to be durable, reliable, and safe. Raceway systems typically consist of raceways, which are channels made of metal or plastic, and fittings, which provide a secure connection between the raceways and other components, such as switches and outlets.

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Answer:

14.12 w /m^2

Explanation:

Determine the heat transfer rate per unit surface area

First step : determine the thermal resistance of the composite wall considering all present forms of heat transfer

Rth = 1 / h₀ + Lp / Kp + Li / Ki  + Lp / Kp  + 1 / hi  --------- ( 1 )

where : h₀ and hi = 5 W/m^2  ,  Li = 50 mm , Ki = 0.046 W/m.k,  Lp = 3 mm,

            Kp = 60 W/m.k  

Insert values into equation 1 above

Rth = 1.487 m^2. K/W

Next : determine the heat gain per unit surface area ( heat transfer rate )

Q = ( To - Ti ) / Rth

   = 21° C / 1.487

   = 14.12 W/m^2

Answer: B, plumb bob

Explanation:

A plumb bob's main job was to establish what is true (ie vertical and perpendicular to a surface,) as well as the secondary task of marking these points.

Compasses are mainly used to draw circles, protractors are used to measure angles, and rulers are used to measuring length.

The finite automata will be: States: q0, q1, Input Symbols: a, b, Start State: q0, Accepting State: q1, Transition Function:q0 → q1 on input a, q0 → q1 on input b, q1 → q1 on input a, q1 → q1 on input b, Grammar wil be: S → aSb | bSa | ε

Finite Automata is a mathematical model of computation used to recognize patterns within a given sequence of inputs. It consists of a set of states, transitions between those states, and a set of input symbols. It is a powerful tool for recognizing patterns and can be applied to a wide range of applications, such as lexical analysis, pattern recognition, and language recognition. Each state within a finite automaton has a unique set of transitions that can be triggered when a certain input symbol is encountered. This allows the machine to move from one state to another, thus recognizing patterns and making decisions based on the input. Finite automata are typically used in computer science and engineering to design and analyze algorithms.

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a) The power transmitted by the belt, is 5.53 hp and (b) the work done in one minute of sanding, in Btu is 37500 Btu.

What is power?
Power is the ability to influence people, events, and outcomes. It is a fundamental element in the human experience, and it has been studied by scholars and philosophers for centuries. Power can manifest itself in many forms, such as political, economic, military, cultural, or social. It is often used to control or dominate others, and it is used to create and maintain systems of inequality and oppression. Power can also be used for good, such as providing people with the resources and ability to make positive changes in their lives and the world around them.

a) Power Transmitted by the Belt = (15 bf) x (1500 ft/min) x (0.2) = 4500 bf-ft/min = 4500 ft-lb/min = 7500 Btu/s = 5.53 hp

b) Work Done in One Minute of Sanding = (15 bf) x (1500 ft/min) = 22500 ft-lb = 37500 Btu

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Technician A is the correct answer. He is correct in saying that after an accident, you should take precautions to avoid it happening again in the future.

First, look for any injuries. If someone is in pain, take care of them.

After that, move your car to a safer location where you can exchange names, addresses, phone numbers, vehicle identification numbers, vehicle license plate numbers, insurance information, and driver's license information.

Finally, take note of the crash site and obtain the names, addresses, and phone numbers of any witnesses. If the vehicles cannot be moved, set up flares or raise your hood to protect the scene.

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The next step in the process is to crystallize the juice. The pale yellow juice is heated until the temperature reaches about 80°C, at which point the sucrose in the juice begins to form into crystals.

What is sucrose?
Sucrose is a type of sugar composed of glucose and fructose molecules bound together. It is a naturally occurring disaccharide found in many plants, where it serves as a form of energy storage. Sucrose is the most common sugar in the human diet and is used in a wide variety of food products. It is found in many processed foods and can be added to foods to enhance flavor. Sucrose is usually extracted from sugar cane or sugar beets, then processed into granulated sugar, which is used in baking or to sweeten drinks.

These crystals are then separated from the liquid in a centrifuge to produce raw sugar crystals. The remaining liquid, known as molasses, is then processed further to remove the remaining sucrose, creating a more viscous dark syrup. The raw sugar crystals are then washed and dried, and are ready to be packaged and sold as raw sugar.

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About 296.5 N of anchoring force is required to keep the elbow in place. About 134.8 is the direction of the anchoring force.

The speed of an object is its magnitude (or value), which is the velocity. The item is traveling in the direction indicated by the velocity vector. Imagine a circle (or, better yet, draw one) and an object traveling along the path it defines.

Units of mass times length over time squared are used to express the strength of a force. The most used unit in metric measurements is the newton (N), which is equal to one-kilogram times one meter over one second squared.

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Answer:

5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm

Explanation:

The total current density, J = drift current density, J' + diffusion current density, J"

J = J' + J"

J' = nμeE where n = electron concentration =  10¹⁶ exp (-x/18) cm³, μ = electron mobility = 960 cm²/V-s, e = electron charge = 1.602 × 10⁻⁹ C and E = electric field

J" = eDdn/dx where e = electron charge = 1.602 × 10⁻¹⁹ C, D = diffusion coefficient = 25 cm²/s and dn/dx = concentration gradient = d10¹⁶ exp (-x/18) cm³/dx = (-10¹⁶/18)exp (-x/18) cm³

So,

J = J' + J"

J = nμeE + eDdn/dx

E = (J - eDdn/dx)/nμe

Since J = 40 A/cm², substituting the values of the variables into the equation, we have

E = (J - eDdn/dx)/nμe

E = [40 A/cm² - 1.602 × 10⁻⁹ C × 960 cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm³ × 960 cm²/V-s × 1.602 × 10⁻⁹ C)

E = [40 A/cm² - 1537.92 × 10⁻⁹ C-cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm² × 1537.92 × 10⁻⁹  C-cm³/V-s)

E = [40 A/cm² + 85.44 × 10⁷ C-cm/V-s exp (-x/18) cm²] ÷ (exp (-x/18) cm² × 1537.92 × 10⁷  C-cm³/V-s)

E = [40 A/cm² ÷ (exp (-x/18) cm² × 1537.92 × 10⁷  C-cm³/V-s)] + [85.44 × 10⁷ C-cm/V-s exp (-x/18) cm² ÷ (exp (-x/18)  × 1537.92 × 10⁷  C-cm²/V-s]

E = [0.026 × 10⁻⁷ A/cm²exp (x/18)    V-s/C-cm³] + 0.0056]

E = [0.026 × 10⁻⁷exp (x/18) V/cm] + 0.0056]

E = 0.056[0.026 × 10⁻⁷exp (x/18) V/cm]/0.056 + 1]

E = 0.056[4.643 × 10⁻⁷exp (x/18) V/cm] + 1]

E = 5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm

To determine whether the marketing campaign will add value to the business, the marketing agency should apply the Present Net Value formula.

A calculation known as the Present Net Value brings all of an investment's future cash flows to the present. The company must identify the revenue totally attributed to the marketing campaign in order to evaluate the campaign marketing strategy as a prospective investment. By doing this, the company will be able to determine the annual inflows (sales) that must be deducted from the outflows (marketing expenses). Every year's net value is discounted at a certain rate, and if the Present Net Value is more than 0, the marketing plan is anticipated to add value to the company. To determine whether the marketing campaign will add value to the business, the marketing agency should apply the Present Net Value formula.

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Answer:

5E22 atoms/cm³

Explanation:

We need to find the number of moles of silicon per cm³

number of moles per cm³ = density/atomic weight = 2.33 g/cm ÷ 28.09 g/mol = 0.083 mol/cm³.

Since there are 6.022 × 10²³ atoms/mol, then the number of atoms of silicon per cm³ = number of atoms per mol × number of moles per cm³

= 6.022 × 10²³ atoms/mol × 0.083 mol/cm³

= 0.4995 × 10²³ atoms/cm³

= 4.995 × 10²² atoms/cm³

≅ 5 × 10²² atoms/cm³

= 5E22 atoms/cm³

Answer:

5.31 × 10⁻⁴⁰ Fm²

Explanation:

Using the Clausius-Mossotti equation

(ε - 1)/(ε + 2) = Nα/3ε₀ where ε = dielectric constant = 1.0015, ε₀ = 8.854 × 10⁻¹² F/m, N = number of molecules of SF6 per unit volume and α = electronic polarizability

So, α = (ε - 1)3ε₀/[(ε + 2)N]

Also

P = (N/NA)RT where P = pressure = 1 atm = 1.013 × 10⁵ Pa, N = number of molecules of SF6 per unit volume, NA = Avogadro's constant = 6.022 × 10²³ /mol, R = molar gas constant = 8.314 J/mol-K and T = room temperature = 25° = 273 + 25 = 293 K

So, N = PNA/RT

= 1.013 × 10⁵ Pa × 6.022 × 10²³ /mol ÷ (8.314 J/mol-K × 293 K)

= 6.100286 × 10²⁸ Pa/mol ÷ (2436.002 J/mol)

= 0.0025 × 10²⁸ molecules/m³

= 2.5 × 10²⁵ molecules/m³

So,

α = (ε - 1)3ε₀/[(ε + 2)N]

α = (1.0015 - 1)× 3 × 8.854 × 10⁻¹² F/m/[(1.0015 + 2)2.5 × 10²⁵ molecules/m³]

α = (0.0015)26.562 × 10⁻¹² F/m/[(3.0015)2.5 × 10²⁵ molecules/m³]

α = 0.039843 × 10⁻¹² F/m/[7.50375 × 10²⁵ molecules/m³]

α = 0.00531 × 10⁻³⁷ Fm²

α = 5.31 × 10⁻⁴⁰ Fm²

There will be several advantages to equipment standardization. Digital solutions accelerate standardization by giving an overview of the field equipment.

By using the most effective and efficient procedures, they aid in accelerating the rate of output. Reduce construction costs overall, especially for big contracts. A machine or piece of equipment can effortlessly perform tasks that are too difficult or delicate for human muscles to complete.

In general, they are used to assemble or disassemble objects (such as hammers and nail guns) (e.g., jackhammers and saws). Hand tools and power tools are two common categories for tools. All non-powered instruments are considered hand tools, such as such as pliers and hammers.

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Answer:

Uber is least comparable to Eventbrite. Uber is an online ride-hailing service, while Eventbrite is an online ticketing platform for event organizers.

Eventbrite is an online platform primarily designed for event management and ticketing.

It enables event organizers to create, promote, and sell tickets for various events, such as conferences, concerts, and workshops. Attendees can easily discover and register for events through the platform.

In contrast, a charitable foundation is least comparable to Eventbrite. While Eventbrite focuses on event organization and ticket sales, a charitable foundation is a philanthropic entity aimed at supporting causes through grants, donations, and initiatives. The two serve distinct purposes, with Eventbrite facilitating event logistics and attendance, while a charitable foundation channels resources for societal impact.

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The ionic radius of Ca²⁺ is 100 pm, K⁺ is 138 pm, Cl⁻ is 181 pm, and S²⁻ is 184 pm, therefore option d is the right choice.

The influence of an ion's nucleus on its electron cloud extends outward to a distance called the ionic radius.

When an atom loses or gains an electron, an ion is created. A cation is formed when an atom loses an electron, and an anion is formed when an atom gains an electron. The ionic radius is the furthest point away from the ion's nucleus that its outermost shell can extend.

A cation's atomic size will be lower than that of its parent atom. Compared to its parent atom, an anion is comparatively large. That's because the net effective nuclear charge gets drowned out by the repulsion between electrons caused by an atom gaining electrons.

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Answer:

adcb i believe the answer is

Answer:

a)  358.8 KJ/kg

b)  0.0977  KJ/K- kg

c)  83.28%

Explanation:

N2 at 300 k. ( use the properties of N2 at 300 k (T1) )

Cp = 1.04 KJ/kg-k , Cv = 0.743 KJ/Kgk ,  R = 0.1297 KJ/kgk , y = 1.4 ,

Given data:

T2 = 645 k

P1 = 1 bar , P2 = 10.5 bar

a)Determine the work input in KJ/Kg of N2 flowing

Winput = h2 - h1  = Cp( T2 - T1 ) = 1.04 ( 645 - 300 ) = 358.8 KJ/kg

b) Determine the rate of entropy in KJ/K- kg   of N2 flowing

Rate of entropy ( Δs ) = Cp*InT2/T1 - R*In P2/P1

                                    = 1.04 * In (645/300) - 0.1297 * In ( 10.5 / 1 )

                                    = 0.0977  KJ/K- kg

c) Determine isentropic compressor efficiency

Isentropic compressor efficiency = 83.28%

calculated using the relation below

( h'2 - h1 ) / ( h2 - h1 ) = ( T'2 - T1 ) / ( T2 - T1 )

where T'2 = 587.314

The  difference in voltage across the two loads is 6 V.

In a series circuit, the total resistance is equal to the sum of the individual resistances. In this case, the total resistance of the circuit is 2 Ω + 4 Ω = 6 Ω.

The current in a series circuit is the same through all of the loads. This means that the same amount of voltage is dropped across each load. Since the power source has a voltage of 12 V, and the total resistance of the circuit is 6 Ω, the current in the circuit can be calculated using Ohm's Law:

I = V/R

= 12 V / 6 Ω

= 2 A.

Since the same current flows through both loads and the same amount of voltage is dropped across each load, there is no difference in voltage across the two loads. Both loads experience a voltage drop of:

12 V / 2

= 6 V.

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A.B's real component is 0.457. Ab is imaginary component 43.67. A/real B's portion is 1.583. A/imaginary B's part is -0.319.

to create a phase transformation in (a substance): to transform alcohol into sugar. To invert or transfer. to assert unauthorized legal title to (personal property).

Consider the following cormplex number.

[tex]$$n=5.6+j 6.6$$[/tex]

Consider the formula for conrplex to polar conversion[tex]$x+j y=r \angle \theta^{\circ}$[/tex]

Where

[tex]$$\begin{aligned}& r=\sqrt{x^2+y^2} \\& \theta=\tan ^{-1}\left(\frac{y}{x}\right)\end{aligned}$$[/tex]

Calculate the magnitude of[tex]$n$.[/tex]

[tex]$$[/tex]

[tex]\begin{aligned}& A=\sqrt{5.6^2+6.6^2} \\& A=8.655\end{aligned}$$[/tex]

Calculate the phase of[tex]$n$.[/tex]

[tex]$$[/tex]

[tex]B=\tan ^{-1}\left(\frac{6.6}{5.5}\right)$$[/tex]

[tex]$$B=49.685^{\circ}$$[/tex]

(b)

Consider the following complex numbers.

[tex]$$\begin{aligned}& A=9.9+j 2.9 \\& B=6.1+j 5.3\end{aligned}$$[/tex]

Calculate[tex]$A \cdot B$.[/tex]

[tex]& A \cdot B=83.36 \angle 57.3^{\circ} \\& \text { Calculate } \frac{A}{B} \\& \frac{A}{B}=\frac{9.9+j 2.9}{6.1+j 5.3} \\& \frac{A}{B}=\frac{9.9+j 2.9}{6.1+j 5.3} \times \frac{6.1-j 5.3}{6.1-j 5.3} \\& \frac{A}{B}=\frac{(9.9+j 2.9)(6.1-j 5.3)}{6.1^2+5.3^2} \\& \frac{A}{B}=1.16-j 0.53 \\[/tex]

[tex]& \frac{A}{B}=\sqrt{1.16^2+0.53^2} \angle \tan ^{-1}\left(\frac{-0.53}{1.16}\right) \\& \frac{A}{B}=1.276 \angle-24.65^n \\& A=8.4 \angle 39^{\circ} \\& B=5.2 \angle 50.4^{\circ} \\& A \cdot B=\left(8.4 \angle 39^{\circ}\right)\left(5.2 \angle 50.4^{\circ}\right) \\[/tex]

[tex]& A \cdot B=(8.4 \times 5.2) \angle 39^{\circ}+50.4^{\circ} \\& A \cdot B=43.68 \angle 89.4^* \\& A \cdot B=43.68 \cos \left(89.4^{\circ}\right)+j 43.68 \sin \left(89.4^{\circ}\right) \\& A \cdot B=0.457+j 43.67 \\&\end{aligned}[/tex]

[tex]$$Calculate $\frac{A}{B}$[/tex]

[tex]$$\begin{aligned}& \frac{A}{B}=\frac{8.4 \angle 39^{\circ}}{5.2 \angle 50.4^{\circ}} \\& \frac{A}{B}=\left(\frac{8.4}{5.2}\right) \angle 39^{\circ}-50.4^{\circ} \\& \frac{A}{B}=1.615 \angle-11.4^{\circ} \\& \frac{A}{B}=1.615 \cos (-11.4)+j 1.615 \sin (-11.4) \\& \frac{A}{B}=1.583-j 0.319\end{aligned}$$[/tex]

Real part of[tex]$A \cdot B$ is $0.457$[/tex]

imaginary part of[tex]$A \cdot B$ is $43.67$[/tex]

Real part of [tex]$\frac{A}{B}$ is $1.583$[/tex]

Imaginary part of[tex]$\frac{A}{B}$ is $1.583$[/tex][tex]$\frac{A}{B}$ is $1.583$[/tex]

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A.B's real component is 0.457. Ab is imaginary component 43.67. A/real B's portion is 1.583. A/imaginary B's part is -0.319.

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__________________________________________________________

Hello! In this question, I will answer the first part of the question, in which we will determine the x, y, and z components for the reaction at joint A in the ball-and-socket.
__________________________________________________________

Explanation:

To better understand what the question entails, we will start off by drawing the free-body diagram to understand the direction of our components. The image is attached below. This will help us solve for our components.

__________________________________________________________

Solve:

To start, we will first solve for the weight of the sign, we will use the formula:

[tex]W=mg[/tex]

Whereas:

Plug in our values into the formula and solve:

[tex]W = 90\cdot9.81=882.9 N[/tex]

Since we now know our weight value, we can solve for our force in the cable BC, expressed as a vector. We will use the formula:

[tex]\bold{T}_{BC}=T_{BC}(\frac{\bold{r}_{BC}}{r_{BC}})[/tex]

Where:

Plug in our values into the formula and solve:

[tex]\bold{T}_{BC}=T_{BC}\bigg(\cfrac{\text{[i - 2j+ 2k] ft}}{\sqrt{(1)^2+(-2)^2+(2)^2}}}\bigg)\\\\\bold{T}_{BC}=T_{BC}\bigg(\cfrac{\text{[i - 2j+ 2k] ft}}{3}}}\bigg)\\\\\text{Simplify}\\\\\bold{T}_{BC}=\frac{1}{3}T_{BC}{\text{i}}-\frac{2}{3}T_{BC}j+\frac{2}{3} T_{BC}k[/tex]

Now, let us solve for our force in the cable BD, also expressed as a vector. Use the formula:

[tex]\bold{T}_{BD}=T_{BD}(\frac{\bold{r}_{BD}}{r_{BD}})[/tex]

Use the same steps from solving for our vector force of cable BC. Plug in the values and solve:

[tex]\bold{T}_{BD}=T_{BD}\bigg(\cfrac{\text{[-2i - 2j+ k] ft}}{\sqrt{(-2)^2+(-2)^2+(1)^2}}}\bigg)\\\\\bold{T}_{BD}=T_{BD}\bigg(\cfrac{\text{[-2i - 2j+ k] ft}}{3}}}\bigg)\\\\\text{Simplify}\\\\\bold{T}_{BD}=-\frac{2}{3}T_{BD}{\text{i}}-\frac{2}{3}T_{BD}j+\frac{1}{3} T_{BD}k[/tex]

We now need to find the moment at A at equilibrium (0). This is known as:

[tex]\sum M_{a}=0 \Rightarrow\bold{r}_{B}\times(\bold{T}_{BC}+\bold{T}_{BD}+\bold{W})=0[/tex]

Whereas:

Plug in values into the equation:

[tex]2\text{j}\times\big[\big(\frac{1}{3}T_{BC}{\text{i}}-\frac{2}{3}T_{BC}j+\frac{2}{3} T_{BC}k\big)+\big(-\frac{2}{3}T_{BD}{\text{i}}-\frac{2}{3}T_{BD}j+\frac{1}{3} T_{BD}k\big)\big]\\+\text{j}\times-882.9\text{k}=0[/tex]

Find the moment about the z-axis to zero. This is known as:

[tex]\sum M_{z}=0\\\\-\frac{2}{3}T_{BC}+\frac{4}{3}T_{BD}=0\\\\\text{Simplify}\\\\T_{BC}=2T_{BD}[/tex]

Now, find the moment about the x-axis to zero. This is known as:

[tex]\sum M_{x}=0\\\\\frac{4}{3}T_{BC}+\frac{2}{3}T_{BD}-882.9=0\\\\\text{We know }T_{BC}=2T_{BD}\text{, plug in }2T_{BD}\text{ in }T_{BC}\\\\\frac{4}{3}\times2T_{BD}+\frac{2}{3}T_{BD}-882.9=0\text{ Solve for }T_{BD}\\\\\frac{10}{3}T_{BD}=882.9\\\\T_{BD}=264.87\text{ N}[/tex]

Now, let us calculate the tension in wire BC.

[tex]T_{BC}=2T_{BD} = 2(264.87) = 529.74\text{ N}[/tex]

Let us calculate the reaction at A by solving for the equilibrium force equation. The formula is:

[tex]\sum F=0\\\\\bold{F}_A+\bold{T}_{BC}+\bold{T}_{BD}+\bold{W}=0[/tex]

Plug in our known information into the equation and simplify.

[tex]\big[(A_xi+A_yj+A_zk)+(\frac{1}{3}T_{BC}{\text{i}}-\frac{2}{3}T_{BC}j+\frac{2}{3} T_{BC}k)+(-\frac{2}{3}T_{BD}{\text{i}}-\frac{2}{3}T_{BD}j\\+\frac{1}{3} T_{BD}k)-981\text{k}\big]=0\\\\\text{Separate by component}\\\\\big[(A_x+\frac{1}{3}T_{BC}-\frac{2}{3}T_{BD})\text{\bold{i}}+(A_y-\frac{2}{3}T_{BC}-\frac{2}{3}T_{BD})\text{\bold{j}}+(A_z+\frac{2}{3}T_{BC}+\frac{1}{3}T_{BD}\\-981)\text{\bold{k}}\big]=0\\\\\text{Plug in known values}\\[/tex]

[tex]\big[(A_x+\frac{1}{3}\times529.74-\frac{2}{3}\times264.87)\text{\bold{i}}+(A_y-\frac{2}{3}\times529.74-\frac{2}{3}\times264.87)\text{\bold{j}}+(A_z+\frac{2}{3}\times529.74+\frac{1}{3}\times264.87-882.9)\text{\bold{k}}\big]=0[/tex]

Now, we can calculate our reactions.

Calculate the reaction at A in the x-direction.

[tex]\sum F_x=0\\\\A_x+\frac{1}{3}\times529.74-\frac{2}{3}\times264.87=0\\\\\boxed{A_x=0\text{ N}}[/tex]

Calculate the reaction at A in the y-direction.

[tex]\sum F_y=0\\\\A_y-\frac{2}{3}\times529.74-\frac{2}{3}\times264.87=0\\\\A_y-529.74=0\\\\\boxed{A_y=529.74\text{ N}}[/tex]

Calculate the reaction at A in the z-direction.

[tex]\sum F_z=0\\\\A_z+\frac{2}{3}\times529.74+\frac{1}{3}\times264.87-981=0\\\\A_z-441.45=0\\\\\boxed{A_z=441.45\text{ N}}[/tex]

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Answer:

[tex]\boxed{\text{A=} < \text{0, 529.74, 441.45} > }[/tex]

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