The first equation is linear, the second equation is nonlinear, the third equation is nonlinear, the fourth equation is nonlinear, the fifth equation is nonlinear, and the sixth equation is nonlinear.
What is equation?
An equation is an expression that contains an equal sign and relates two or more mathematical quantities. It typically consists of constants, variables, and symbols, and can be written in different forms such as standard form, slope-intercept form, and factored form. Equations are used to describe relationships between variables, and they can be used to solve a wide range of problems, from basic arithmetic to advanced calculus and physics. Equations are also used to model real-world phenomena, such as electricity, kinematics, and quantum mechanics. By studying equations and their solutions, we can gain a deeper understanding of the physical world around us.
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WHAT IS MEANT BY BJT AND FUNCTION OF BJT
Answer:
A Bipolar Junction Transistor, or BJT, is a solid-state device in which the current flow between two terminals (the collector and the emitter) is controlled by the amount of current that flows through a third terminal (the base).
The main basic function of a BJT is to amplify current it will allow BJTs are used as amplifiers or switches to produce wide applicability in electronic equipment include mobile phones, industrial control, television, and radio transmitters. There are two different types of BJTs are available, they are NPN and PNP.
Compute the atomic density (the number of atoms per cm3 rather than mass density g/cm3) for a perfect crystal of silicon at room temperature, given that the room temperature density and atomic weight of silicon are 2.33 g/cm3 and 28.09 g/mol, respectively.
Hint: you do NOT need any information about the crystal structure of silicon to solve for this quantity, based on the information provided in this particular problem.
Be sure to use values exactly as given and do not round until the final answer.
Use 6.022x1023 , exactly, for Avogadro's Number.
Answer Format: XEX where EX stands for *10x
Units: atoms/cm3
Example: So for an answer of 158123.126 you would type: 2E5 since only a whole number is prescribed for the prefix.
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
Which of the following steps should a high school teacher take first when introducing procedures at the beginning of the year: A. Explaining the details of the procedures
B. Correcting misunderstandings about the procedures
C. Reinforcing effective use of the procedures
D. Practicing the procedures regularly with the class
Option A is correct because the details of the procedures should be explained before they are practised at this age level.
Options B, C, and D are incorrect because, while these steps are necessary, students must first understand the procedures.
How to teach procedures to your students?
The key to making your classroom run smoothly and efficiently is to teach procedures. If you take the time to teach your class how to do things, I guarantee you will have more time to focus on academics in the long run.
STEP 1 – PROCEDURES START WITH YOU
Before you can teach your students procedures, you must first envision how you want your classroom to look, sound, and feel on a daily basis. This means that you must consider these issues before the start of the school year.
STEP 2 – PUT YOUR PROCEDURES INTO SIMPLE STEPS
Once you've decided on the procedure that will get you to your ideal classroom, it's time to break it down into simple, easy-to-follow steps. When you do this, keep your students in mind. The language and number of steps will differ if you teach Pre-K or Kindergarten versus 3rd, 4th, or 5th grades. I've always found the K.I.S.S. method to be effective. Keep it as simple as possible.
STEP 3 – TEACH THE PROCEDURES
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raw sugar cane is taken into a process to create sugar, which is essentially sucrose. the raw cane is approximately 16% sucrose, 63% water, and the rest fiber by mass. juice from the cane is extracted by passing the cane through a series of crushers. about 5% extra mass of water is added to the sugar cane prior to this step to help in the extraction process. the crushed cane and liquid juice is sent to a filter press that creates a cake that contains 4% of the weight of the cane juice, which has a composition similar to the overall non-fiber content of the raw cane. the filtrate is sent to an evaporator where enough water is evaporated to obtain a pale yellow juice that is 41% water. a
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.
What is crusher?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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raw sugar cane is taken into a process to create sugar, which is essentially sucrose. the raw cane is approximately 16% sucrose, 63% water, and the rest fiber by mass. juice from the cane is extracted by passing the cane through a series of crushers. about 5% extra mass of water is added to the sugar cane prior to this step to help in the extraction process. the crushed cane and liquid juice is sent to a filter press that creates a cake that contains 4% of the weight of the cane juice, which has a composition similar to the overall non-fiber content of the raw cane. the filtrate is sent to an evaporator where enough water is evaporated to obtain a pale yellow juice that is 41% water. a
The next step in the process is to purify the juice. This is done by adding calcium hydroxide which removes impurities and non-sucrose components. The juice is then heated and concentrated in vacuum pans.
What is vacuum?
Vacuum is an empty space devoid of matter. It is a space that is completely void of any matter, including molecules, atoms, and subatomic particles. It has zero pressure and is a state of matter considered to be more rare than a gas, liquid, or solid. Vacuums can be generated artificially in a laboratory setting or can occur naturally in the absence of air or other gasses. Vacuum environments are used in many scientific and industrial applications and are especially important in the field of physics, where they are used to study the behavior of matter on a microscopic scale.
This process drives off the water and forms a thick syrup containing 85-95% sucrose. The syrup is then seeded with sugar crystals and further heated in a process called inversion. Finally, the sugar is packaged for sale or further processed into other forms of sugar such as brown sugar, powdered sugar, and so on.
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Nitrogen (N2) at 1 bar, 300 K enters a compressor operating at steady state and is compressed adiabatically to an exit state of 10.5 bar, 645 K. The N2 is modeled as an ideal gas and kinetic and potential energy effects are negligible. Determine the work input, in kJ per kg of N2 flowing, the rate of entropy production, in kJ/K per kg of N2 flowing, and the isentropic compressor efficiency.
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
a 90° elbow in a horizontal pipe is used to direct water flow upward at a rat of 40 kg/s.
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.
What are the object's size and direction?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.
How do you calculate the force's magnitude?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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The density of seawater at a free surface where the pressure is 98 kPa is approximately 1030 kg/m3. Taking the bulk modulus of elasticity of seawater to be 2. 34 109N/m2 and expressing variation of pressure with depth z as dp= rgdz determine the density and pressure at a depth of 2500 m. Disregard the effect of temperature. Recall that:(i) The bulk module of elasticity is defined as: (ii) Density is not assumed as constantin this problem
The pressure of seawater will be 2.14*107 N/m2 and the density will be 8.53*103 kg/m3.
What is pressure?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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Question 1
(a) A conductor has a constant current of 2 A, how many electrons pass a fixed point on
the conductor in one 30 seconds?
(b) What is the total current of energy source supplying 40 C charge over 10 s? Given the
total energy of 1000 J as heat, compute the voltage drop across the terminal of the
energy source
(c) Calculate the equivalent resistance between points a and b of Figure 3. If the input
current at port ‘a’ is 2 A, what are the voltage supply and the total average power?
the the rectangular components of acceleration for a particle are ax = 3t and ay= (30-10t) where a is in m/ s^2 . if the particles start from rest at the origin. find the radius of curvature of the path at the instant 2 second
Answer:
i like icecream
Explanation:
A series circuit has a power source with a voltage of 12 V and two electrical loads. One load has a resistance of 2 Ω, and the other has a resistance of 4 Ω. What is the difference in voltage across the two loads?
The difference in voltage across the two loads is 6 V.
What is the circuit about?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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Because of its high dielectric strength, SF6 (sulfur hexafluoride) gas is widely used as an insulator and a dielectric in HV applications such as HV transformers, switches, circuit breakers, transmission lines, and even HV capacitors. The SF6 gas at 1 atm and at room temperature has a dielectric constant of 1.0015. The number of SF6 molecules per unit volume Ncan be found by the gas law, P= (N/NA)RT.
Required:
Calculate the electronic polarizability αeof the SF6 molecule.
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
The power supply of a 3phase induction motor is 40kw and the corresponding stator losses are 1.5kw. Calculate the total mechanical power developed below
Two different kinds of losses can happen in a three-phase induction motor. These losses are variable losses that are constant or fixed losses. Fixed or Constant Losses Consta.
Exactly how are stator losses determined?Stator losses, including as stator iron loss and stator copper loss, are financed in part by this power input. Rotor input is provided with the leftover power, or (input electrical power - stator losses). Thus, rotor input P2 equals Pin minus stator losses (stator copper loss and stator iron loss).
What are the induction motor's three-phase losses?Fixed losses, Copper losses, and stray losses are a few types of losses that can occur in three-phase induction motors. Core losses, bearing friction losses, brush friction losses (in wound rotor motors), and windage losses make up the majority of these losses.
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Significance of a research report
Explanation:
A research report is a well-crafted document that outlines the processes, data, and findings of a systematic investigation. It is an important document that serves as a first-hand account of the research process, and it is typically considered an objective and accurate source of information.
(1) to build knowledge and facilitate efficient learning, (2) to understand various issues, (3) to know the truth and prove lies, and (4) to seek opportunities among others
An engineer follows the rigorous design procedure for end plate connections according to the ASD method. So far it has been determined that the thickness of the end plate is 0.5 in. while its ultimate tensile strength is 100 kips. Four holes which are 0.875 in. in diameter are to be drilled into the plate to accommodate bolts. From these values, what is the factored bearing deformation strength per bolt
Answer:
105 kips
Explanation:
Determine the factored bearing deformation strength per bolt
we can determine this using the relationship below
Bearing deformation strength = C * Area * Fl --------- ( 1 )
Fl = factored load = 100 kips
Area ( bearing area ) = diameter of bolt * thickness of end plate
= 0.875 * 0.5 = 0.4375 in^2
C = 2.4 ( constant for bolt holes not drilled at edges )
back to equation 1
2.4 * 0.4375 * 100
= 105 kips
disc type parking brake mechanically applies the brake pads againts the disc rotor when the actuating lever causes the check balls to ride up the ball ramp
Disc-type automotive braking systems mechanically apply the brake pads against the disc rotor when the actuator causes the control balls to move up the ball ramp.
Automotive disc braking systems are a safe and reliable form of braking. They are designed to stop the vehicle quickly and safely. These braking systems work by applying pressure from the brake discs to the brake discs mounted on the wheel axle.
This in turn causes the discs to press against the brake calipers, which in turn are applied to the discs. This action results in safe and reliable braking.
These braking systems also have a mechanical parking function, which is activated by the actuator lever. When the lever is activated, the control balls are moved up the ball ramp, which causes the brake discs to be applied to the rotor to ensure safe braking.
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define atom according to general chemistry
8. Find the volume of the figure shown below: * V=L x W x H 7 cm 2 cm 2 cm
The design of a concrete mix requires 1173 kg/m3 of gravel in dry condition, 582 kg/m3 of sand in dry condition, and 157 kg/m3 of free water. The gravel available at the site has a moisture content of 0.9% and absorption of 1.5%, and the available sand has a moisture content of 1.2 and absorption of 1.5%. What are the masses of gravel, sand, and water per cubic meter that should be used at the job site
Answer:
- the weight of the gravel is 1183.56 kg/m³
- the weight of sand is 588.98 kg/m³
- the weight of water is 165.784 kg/m³
Explanation:
Given the data in the question;
mixture content of the gravel = 1173 kg/m³
sand content = 582 kg/m³
free water content = 157 kg/m³
moist of gravel = 0.9%
absorption of gravel = 1.5%
moist of sand = 1.2%
absorption of sand = 1.5%
masses of gravel, sand, and water per cubic meter that should be used at the job site ?
To get the weight of moist gravel, we use the following equation;
Weight of moist gravel = content of gravel × ( 1 + moist of gravel )
we substitute
Weight of moist gravel = 1173 × ( 1 + 0.9%)
Weight of moist gravel = 1173 × ( 1 + 0.009)
Weight of moist gravel = 1173 × 1.009
Weight of moist gravel = 1183.56 kg/m³
Therefore, the weight of the gravel is 1183.56 kg/m³
To get weight of the sand, we use the following formula;
Weight of sand = sand content × ( 1 + moist of sand )
we substitute
Weight of sand = 582 × ( 1 + 1.2% )
Weight of sand = 582 × ( 1 + 0.012 )
Weight of sand = 582 × 1.012
Weight of sand = 588.98 kg/m³
Therefore, the weight of sand is 588.98 kg/m³
To get the weight of mix water ; we use the following equation;
[tex]Mix-Water_{weight[/tex] = water content - gravel content( moist of gravel - absorption of gravel) - sand content( moist of sand - absorption of sand )
so we substitute
[tex]Mix-Water_{weight[/tex] = 157 - 1173( 0.9% - 1.5%) - 582( 1.2% - 1.5% )
[tex]Mix-Water_{weight[/tex] = 157 - 1173( 0.009 - 0.015) - 582( 0.012 - 0.015 )
[tex]Mix-Water_{weight[/tex] = 157 - 1173( -0.006 ) - 582( -0.003 )
[tex]Mix-Water_{weight[/tex] = 157 + 7.038 + 1.746
[tex]Mix-Water_{weight[/tex] = 165.784 kg/m³
Therefore, the weight of water is 165.784 kg/m³
(text 2. 36) A belt sander has a belt speed of 1500 ft/min. The coefficient of friction between the sander and the plywood being finished is 0. 2. If the downward (normal) force on the sander is 15 bf, determine (a) the power transmitted by the belt, in Btu/s and hp, and (b) the work done in one minute of sanding, in Btu
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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The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fiberglass insulation of thermal conductivity ki 0.046 and thickness Li 50 mm and steel panels, each of thermal conductivity kp 60 and thickness Lp 3 mm. If the wall separates refrigerated air at T,i 4 C from ambient air at T,o 25 C, what is the heat transfer rate per unit surface area
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
An airplane is flying at a standard altitude of 5 km. A pitot tube mounted at the nose measures a stagnation pressure of 0. 957 bar. Assume the airplane is flying at high subsonic speed and flow is compressible.
Required:
Calculate the velocity of airplane
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 which type of architectural drawing:
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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Determine the x, y, z components of reaction at the ball-and-socket joint A.
Determine the x, y, z components of the moments where the wing is fixed to the fuselage A.
The sign has a mass of 90kg with center of mass at G.
(Figure 1)
__________________________________________________________
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:
m = mass (90)g = gravity (9.81)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:
[tex]\bold{r}_{BC[/tex] is coordinate B subtracted from the coordinate C[tex]r_{BC}[/tex] is the magnitude of BCPlug 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:
[tex]\bold{T}_{BC}=\big(\frac{1}{3}T_{BC}{\text{i}}-\frac{2}{3}T_{BC}j+\frac{2}{3} T_{BC}k\big)[/tex][tex]\bold{T}_{BD}=\big(-\frac{2}{3}T_{BD}{\text{i}}-\frac{2}{3}T_{BD}j+\frac{1}{3} T_{BD}k\big)[/tex][tex]\bold{W}=-882.9\text{k}[/tex][tex]\bold{r}_{B}=2\text{j}[/tex]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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A flexible pavement has a structural number of 6. If a 36,000 pound single axle is being loaded onto the pavement, how does it compare to a 18,000 pound single axle
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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You are designing a highway to AASHTO guidelines on rolling terrain where the design speed will be 65 mi/h. At one section, a 1.25% grade and a -2.25% grade must be connected with an equal-tangent vertical curve. Determine the minimum length of curve to meet SSD requirements
The minimum length of the curve meeting the SSD requirements is 643.72 ft.
What is SSD?
The Stopping Sight Distance (SSD) is the smallest sight distance that is accessible to a driver on a highway at any location long enough to allow the driver to safely stop a vehicle driving at design speed without colliding with any other obstruction.It is a crucial component in traffic engineering.The formula for SSD is given as, [tex]SSD=vt+\frac{v^{2} }{2g(f \pm \frac{n}{100}) }[/tex]From the given question, we have the grades, [tex]g_{1}=+1.25%[/tex], [tex]g_{2}=-2.25%[/tex], and the design speed, [tex]v=65[/tex] mi/h
So, [tex]SSD=vt+\frac{v^{2} }{2g(f \pm \frac{n}{100}) }\\\implies SSD=1.47(65)(2.5)+\frac{65^{2} }{30(0.347826 \pm \frac{1.25}{100}) }\\\implies SSD=630'[/tex]
The length of the vertical curve is given as, [tex]L=2(SSD)-\frac{2158}{A}[/tex]
When SSD>L, we have\
[tex]L=2(630)-\frac{2158}{-2.25-1.25}\\\implies L=1876.57 ft[/tex]
When SSD<L, we have
[tex]L=\frac{A(SSD)^{2} }{2158} \\\implies L=\frac{(-2.25-1.25)(630)^{2} }{2158} \\\implies L=643.72 ft[/tex]
Hence, the minimum length of the vertical curve is 643.721 ft.
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Look at the following statement. while (++x < 10) Which operator is used first? ++ Neither. The expression is invalid. O both ++ and < operators are used at the same time.
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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which condition normally lowers the water table
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.
The electron concentration in silicon at T = 300 K is given by
n(x) = 10^16 exp (-x/18) cm3
where x is measured in m and is limited to 0< or is equal to x < or is equal to 25 m. The electron diffusion coefficient is Dn = 25 cm2/s and the electron mobility is mun = 960 cm2/V-s. The total electron current density through the semi-conductor is constant and equal to Jn = 40 A/cm2. The electron current has both diffusion and drift current components. Determine the electric field as a function of x-bar which must exist in the semi-conductor.
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
raw sugar cane is taken into a process to create sugar, which is essentially sucrose. the raw cane is approximately 16% sucrose, 63% water, and the rest fiber by mass. juice from the cane is extracted by passing the cane through a series of crushers. about 5% extra mass of water is added to the sugar cane prior to this step to help in the extraction process. the crushed cane and liquid juice is sent to a filter press that creates a cake that contains 4% of the weight of the cane juice, which has a composition similar to the overall non-fiber content of the raw cane. the filtrate is sent to an evaporator where enough water is evaporated to obtain a pale yellow juice that is 41% water. a
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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