The load choices that are available in the question are:
three 6.8v zeners that would give 3 x 6.8-20 volts. This has the resistance of 30 ohms.The four 5.1 V zeners that would provide 4 x 5.1 20.4 volts. The resistance would be 100.How to determine the load choicesa. The 6.8 Zener diode
what is required would be 3 zener diodes. These would be able to provide 3 x 6.8 = 20. 4 output
The resistance would be 3 x 10 ohms = 30 Ohms.
b. For the 5.1 v zener diodeThe requirement here would be 4 zener diodes. This would have to provide 4 x 5.1 = 20.4 volts of output.
The resistance that it would have to give would be 4 x 25 = 100 ohms of resistance.
Therefore from the calculations that we have above we would have to conclude that the load regulation that is here without R would be
30 ohms for the case of a , while it would have to be 100 ohms for the case of b.
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The major advantage of using compound joint snips over a single joint tool is increased. A. flexibility B. mechanical advantage C. cut length D. control
The major advantage of using compound joint snips over a single joint tool is option A: flexibility.
What are compound action snips used for?Standard compound-action snips are known to be a form of a hand tool that is said to be made to cut steel or softer materials, yet it is not harmful to use them sometimes on stainless steel.
Note that the key or the major merit or benefit of using compound joint snips than the use of a single joint tool is due to the fact that a person can be able use these pivot points to make their cut very easy through sheets of metal with the use of small effort.
Hence, option A is correct.
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Donald is installing a fuse on a neutral. In a residential, 120 V, 20 A  Circuit, what should the fuse be rated? A. If you should never be installed in the neutral. B.40A C.20 slow-blo D.20 A
The location at which a fuse should be installed in the 120 V, 20 A, residential circuit is in the live wire on the circuit, not in the neutral wire. The correct option is therefore;
A. A fuse should never be installed in the neutral.
What is the function of a fuse?The function of an electric fuse, which is a safety device, is to provide protection from an over flow of current in the circuit.
Generally, an electric fuse consists of a metal wire or filament that melts, due to its rise in temperature when excessive current or current at an unsafe level flows in the circuit, thereby opening the circuit, to protect the circuit and its components.
The effect of excessive or over current in a circuit is that it causes the circuit component to heat up and burn, such that the circuit and device stops functioning, and in some cases, may cause a fire.
The fuse, which is a circuit safety device, should be the first contact of the current.
Therefore;
The location of a fuse should be at the entrance point of current to the load which is the live wire.The fuse should not be installed on the neutral wire, gives that the burning of the fuse in the neutral, in the event of an over current, leaves the high current in the circuit, which can cause unwanted damage to the circuit.
The correct option is therefore option A;
A. A fuse should never be installed in the neutral
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Enzo’s balance sheet for the month of July is shown.
Enzo’s Balance Sheet (July 2013)
Assets
Liabilities
cash
$600
credit card
$4,000
investments
$500
student loan
$2,500
house
$120,000
mortgage
$80,000
car
$6,000
car loan
$2,000
Total
$127,100
Total
$88,500
Which expression finds Enzo’s net worth?
127,100 dollars minus 88,500 dollars
127,100 dollars divided by 88,500 dollars
88,500 dollars + 127,100 dollars
88,500 dollars minus 127,100 dollars
If Enzo’s balance sheet for the month of July is has both assets and liabilities. The expression that will finds Enzo’s net worth is: A. 127,100 dollars minus 88,500 dollars .
What is Net worth ?Net worth can be determine by deducting the assets of a company by its liabilities which in turn implies that a company or an organization will tend to known their net worth after deducting their financial obligation (debt) from their assets .
Using this formula to find the net worth
Net worth = Assets -Liabilities
Where :
Assets = $127,100
Liabilities = $88,500
Let plug in the formula
Net worth = $127,100 -$88,500
Net worth = $38,600
Hence,
127,100 dollars minus 88,500 dollars .
= $38,600
Therefore the company would have to record their net worth in the amount of $36,800 making option A the correct option because assets minus the liabilities would give us $36,800.
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deduce the relationship between e.m.u and e.s.u in technology .
In the CGS system, the unit of charge is the charging unit (ESU). Also known as "Statistical Pendant" (StatC). In the CGS system, the load unit is the electromagnetic unit (E.M.E.).
The e.s.u. of charge, also known as franklin or statcoulomb, is the charge such that two similar q=1statC charges at a space of 1cm from each other exert an electrostatic force of 1dyn on each other.
The e.m.u. of current, also called the biot or abampere, is the current such that two infinitely-long straight, parallel conductors carrying 1abA of current and separated by 1cm exert a magnetostatic force of 2dyn on each other.
The relations between these units are such that
[tex]\frac{1 statC}{1 abA * 1s} = \frac{1 statC}{1abC} = \frac{1}{C} = \frac{1 statA}{1abA} = \frac{\frac{1 statC}{s} } {1 abA}[/tex]
where c is the speed of light.
The ESU and EMU systems of electromagnetic units are different and they should generally be considered separate and independent (if relatively similar), and they do not coincide with the gaussian set of electromagnetic units.
For example, since the electrical displacement vector D is defined as [tex]E + 4\pi P[/tex] in the ESU system and [tex]\frac{1}{c^{2} } E + 4\pi P[/tex] the EMU system, it is not possible to exchange the formulas of one system for another without using a formula dictionary like the one at Jackson's end. There is not. classical electrodynamics.
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a 15 kw cooling load is to be served by operating an ideal vapor-compression refrigeration cycle with its evaporator at 360 kpa and its condenser at 800 kpa. calculate the refrigerant mass flow rate and the compressor power requirement when refrigerant-134a is used.
When refrigerant-134a is used, the refrigerant mass flow rate is 0.0952kg/s, and the compressor power requirement is 1.659kw
Part a
Refrigerant mass flow rate:
From the steam table refrigerant-134a, we have the following variables:
[tex]h_{1}[/tex] = 252kj/kg
[tex]h_{2}[/tex] = 270.43kj/kg
[tex]h_{3} = h_{4} = 95.47kj/kg[/tex]
Cooling load = 15kw
Now, refrigerator mass flow rate (m)= [tex]\frac{cooling load}{h_{1} -h_{4} }[/tex]
= [tex]\frac{15}{253-95.47}[/tex]
=0.0952kg/s
Part b
Compressor power requirement ([tex]W_{c}[/tex])
= [tex]m(h_{2} -h_{1} )[/tex] , where m is 0.0952kg/s
=0.0952(270.43-253)
=1.659kw
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What does geothermal mean
Answer:
(adjective)
produced by the internal heat of the earth.
{thermal means heat}
what does the hall-petch equation tell you about the relation between the yield strength of a material and the size of the grain in that material? what is the reason behind this relation?
According to the Hall-Petch connection, by lowering grain size, we could make materials stronger than their own theoretical strength.
In fact, their strength rises with decreasing grain size until it reaches a peak at about 20–30 nm. The yield strength is further decreased when the grain size grows by annealing at higher temperatures, but further advancement in tensile elongation is constrained. Be aware that ductility increases slightly when grains are refined from 2 to 1 micrometers in the micrometer-grained scale. strength, ductility, and hardness. Nanocrystalline materials exhibit a significant increase in hardness and strength compared to their coarser-grained counterparts as a result of Hall-Petch strengthening (increase in hardness associated with a reduction in average grain size).
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3 4/5÷2/5 as a fraction
Answer:
9 1/2
Explanation:
3 4/5 is 3.8
2/5 is 0.4
divide 3.8 by 0.4 you get 9.5 which is 9 1/2 in a fraction
a turbine is supplied with 0 6 m3 s of water from a 0.3 m diameter pipe; the discharge pipe has a 0.4 m diameter. determine the pressure drop across the turbine if it delivers 60 kw
The pressure drop across the turbine if it delivers 60 kw is 75.4KPa.
The task of providing usable output shaft power to drive the propeller falls on the turbine section of the gas turbine engine. It must also deliver energy to run the compressor and other engine accessories. This is accomplished by expanding the gas at high pressure, temperature, and velocity and transforming the resulting gaseous energy into mechanical energy in the form of shaft power.
The turbine needs a significant volume of air to generate the required amount of electricity. The compressor provides this volume of air by pulling it into the engine and compressing it to provide high-pressure air for the turbine.
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how do you draw this
Answer:
I could draw it but I cannot see the dimensions clearly. Also, be precise in question. In what projection are you drawing it.
If the Poisson’s ratio of a 5 mm X 5 mm titanium alloy pin is 0.31 and it is elastically loaded in tension from 100 mm to 105 mm. With the aid of a sketch, calculate the new side dimension
The new dimensions of the titanium alloy pin will be that the width is 0.0775 mm and the length is 4.9225m.
What is Poisson's ratio?The Poisson's ratio is the proportion of a material's change in width per unit width to its change in length per unit length due to strain. In order for a stable, isotropic, linear elastic material to have a positive Young's modulus, shear modulus, and bulk modulus, the Poisson's ratio must be between 1.0 and +0.5. Poisson's ratio values for the majority of materials fall between 0.0 and 0.5.
The formula for the longitudinal strain is:
= Change in length / Initial length
Based on the information, the longitudinal strain will be:
= 105 - 100 / 100
= 0.05
Poisson ratio will be illustrated as the change in the width divided by the longitudinal strain.
0.31 = ∆w/5 / 0.05
∆w = 0.0775 mm
New side length will be the difference in the changes in the dimensions. This will be:
= w - ∆w
= 5 - 0.0775
= 4.9225m
In conclusion, the length is 4.9225m.
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superheated steam enters a nozzle that has an inlet diameter that measures 2.5cm and an outlet diameter that measures 1 cm. its outlet velocity has been measured at 30 m/s. the steam that enters the nozzle is at 6508c and 1350 kpa and the steam that exits the nozzle is at 4008c and 100 kpa.
A steam nozzle is a channel or duct with a cross-sectional area that varies gradually and is used to transform the heat energy of steam into kinetic energy. The nozzle's shape is created to convert energy with the least amount of loss possible.
Steam loses both pressure and heat as it travels through the nozzle. The Rankine area is equal to the work completed, which is equal to the adiabatic heat decrease. Steam passing through nozzles can be thought of as expanding adiabatically. The gas's speed rises to supersonic (Mach number >1) as it travels through the diverging nozzle. If the flow is sonic at the throat, the flow rate is at its highest for the particular nozzle.
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1 .8 A capillary tube is immersed vertically in a water container. Knowing that water (3) starts to evaporate when the pressure drops below 2 kPa, determine the maximum capillary rise and tube diameter for this maximum-rise case. Take the contact angle at the inner wall of the tube to be 6 0 and the surface tension to be 1.00 N/m
The maximum capillary rise and tube diameter for this maximum-rise case will be d=0.414× 10⁻⁴ m.
What do you mean by tube?
A tube, also known as tubing, is a long hollow cylinder that is used to transport fluids (liquids or gases) or to protect electrical and optical cables and wires.
Given that, P = 4 KPa
Contact angle = 6°
Surface tension = 1 N/m
Lets assume that atmospheric pressure = 100 KPa
Lets take that density of water = 1000kg/m³
So the capillarity rise h
h=ΔP/ρg
h= (100×1000-4×1000)/(1000×10)
h= 9.61 m
We know that for capillarity rise h
h=2σcosθ/rρg
r = 2σcosθ/hρg
r = (2×1cos4°)/(9.61×1000×10)
r = 0.207×10⁻⁴m
d=0.414× 10⁻⁴ m
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2. Local governments, communities, and the individuals that live there don't have an implied right to know about
the hazards around them.
A) True
B)False
when assembling various shaped pieces together without marring the workpiece, use a A. chain clamp
B. chain wrench
C. spanner wrench
D. strap wrench
Answer:
Strap wrench (I think)
Explanation:
The strap doesnt have any rough edges so it shouldn't mark the workpiece (assuming that is what you meant when you said 'marring'). I would recommend to wait for some other answers though since i haven't studied this yet :)
all brake lights are dimmer than normal. technician a says that bad bulbs could be the cause. technician b says that high resistance in the brake switch could be the cause. which technician is correct?
When all brake lights are dimmer than normal then technician a says that bad bulbs could be the cause, and technician b says that high resistance in the brake switch could be the cause, then the correct technician is technician b
Brake lights serves an important safety function in a vehicle. When the driver presses the break pedal, break lights supplies power to the signal lights at the back of the vehicle to warn other drivers that the vehicle has slowed.
Brake lights can all go dim than normal when there are loose wires in the break, making the brake switch to have high resistance. However, all the brake lights can not be dim than normal if there are some bad bulbs as this will only make them not light at all
Hence, technician b is right.
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Find the average of two numbers given by the user.
What the question wants is to write a code that would find and display the average of two numbers given by a user.
The code or program has been written and has been given below in C + +
The Program#include <iostream>
using namespace std;
int main() {
int a, b, sum;
double avg;
cout << "Enter the first integer number: ";
cin >> a;
cout << "Enter the second integer number: ";
cin >> b;
sum = a + b;
avg = (double)sum / 2;
cout << "\nThe average of your numbers is: " << avg << "\n";
return 0;
}
The Output:Enter the first integer number: 2
Enter the second integer number: 4
The average of your numbers is: 3
A simple explanation of the code is that it makes use of mathematical operators to perform the calculations by first adding up the numbers and then finding the average of the two numbers by dividing the sum of the numbers with two which is the number of elements.
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The metal with the highest Young's modulus
technician a says that variable valve timing allows the engine’s piston displacement to be increased or decreased. technician b says that in-block cams usually include variable valve timing. who is correct?
When technician a says that variable valve timing allows the engine’s piston displacement to be increased or decreased, and technician b says that in-block cams usually include variable valve timing, then both of them are correct.
In an engine, a variable valve timing allows the engine’s piston displacement to increased or decreased to provide better operating conditions to engine. The reason is if the engine piston displacement is increases or decreases it allows the air to the engine which can increase the RPM of the engine.
In an engine in which the block cam is used, the variable valve timing is present. The reason is the timing gap provided by the cam to the valves is variable.
Here, the technician A says variable valve timing allows the engine’s piston displacement to increased or decreased and technician B says that in block cams usually include variable valve timing. So, both technician A and B are correct.
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a design engineer is helping to ensure that the dependencies within her area of expertise are properly defined on the project. the design of several deliverables must be complete before manufacturing can begin. this is an example of what type of dependency?
The given example in this question is a type of discretionary dependency. It states that the design of several deliverables must be completed before starting manufacturing. So option A is correct answer.
In project management, the dependencies show the relationship of the preceding task to the succeeding task. A task can have many preceding and succeeding tasks. Furthermore, there are three different types of dependencies that are mostly used in project management. These dependencies are discretionary, external, and mandatory.
Discretionary dependency is also known as soft logic. It shows how teams working on a project anticipate the work to be completed. It allows the teams working on the project to optimize the flow of work throughout the project life cycle. It also utilizes the best practices and methodologies based on the team and project manager’s experience.
In the given scenario of the question, the design engineer based on her area of expertise properly defined on the project. She may decide based on her areas of expertise that all other deliverables must be completed before manufacturing can begin.
While the other options are incorrect because:
Mandatory dependency defined that a particular task or activity must be carried out at a specific time. While the external dependency takes input from an external source before proceeding a task.
The complete question is given below:
“ a design engineer is helping to ensure that the dependencies within her area of expertise are properly defined on the project. the design of several deliverables must be complete before manufacturing can begin. this is an example of what type of dependency?
A. Discretionary dependency
B. External dependency
C. Mandatory dependency
”
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primary u.s. interstate highways are numbered 1-99. odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. thus, i-405 services i-5, and i-290 services i-90. note: 200 is not a valid auxiliary highway because 00 is not a valid primary highway number. given a highway number, indicate whether it is a primary or auxiliary highway. if auxiliary, indicate what primary highway it serves. also indicate if the (primary) highway runs north/south or east/west.
There is a photo attached with the code. Result: print ("0 is not a valid interstate highway number")
H is equal to int("Enter the highway number: "); if (h>=1 and h=99) take highway number If (h%2==0) for principal highway:
"I-%d is primary, moving eastward and westward,"%h, print #otherwise, even highway number:
print("I-%d is principal, travelling north/south"%h) #for odd road number elif(h>=100 and h=999): supplementary highway for
aux=str(h) #create a string to retrieve the rightmost number.
l=len(aux) val = aux[l-2] #find the length +aux[l-1] If (h%2==0): print("I-"+aux+" is auxiliary,"+"serving I-%d, going east/west"%h) else: print("I-"+aux+" is auxiliary,"+"serving I-%d, going north/south"%h) elif (h==0): print("I-"+aux+" is auxiliary,"+"serving I-%d, going east/ print #for 0 highway number ("0 is not a valid interstate highway number")
if not, pass
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are bonded to the system grounding conductor to provide a low impedance path for fault current that will facilitate the operation of over current devices underground fault conditions.
In order to clear the ground fault, the system bonding jumper offers a low-impedance fault-current path to the electrical supply source.
It refers to service entry equipment and its connected and interconnected parts; in other words, one system conductor is grounded to stabilize the voltage to grounding during normal operation and to reduce voltages caused by lights, line surges, or unintended contact with higher voltage lines. The primary function of this wire is to guarantee the provision of a low-impedance conduit for ground-fault current to return to the utility supply transformer or source and to permit overcurrent device operation during a ground-fault occurrence. When the Code refers to a "low impedance path," The key concept is low opposition or impedance; it refers to a conduit for current to travel on that gives less resistance to current flow, whether it be fault current or normal current.
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the lever is attached to the shaft a using a key that has a width d and length of 24 mm .if the shaft is fixed and a vertical force of 200 n is applied perpendicular to the handle, determine the dimension d if the allowable shear stress for the key is τ
By torque, the allowable dimension d is 5.95 mm.
We need to know about torque to solve this problem. Torque is the rotational equivalent of linear force. It can be determined as
τ = F x r
where τ is torque, F is perpendicular force and r is radius.
From the question above, the parameter given are
F = 200 N
r = 250 mm
x = 24 mm
a = 20 mm
τallow = 35 MPa
The equation of torque will be
Fa . a = F . r
Fa . 0.02 = 200 . 0.25
Fa = 5000 N
τallow = F / A
τallow = F / x.d
35000 = 200 / 0.024.d
d = 5.95 mm
Hence, the dimension d is 5.95 mm
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a solid steel shaft 3 m long is transmitting 12 mw at 400 rev/min. the working conditions to be satisfied by the shaft are: • the shaft must not twist more than 0.015 radian on a length of 10 times the diameter, i.e., 10d • the maximum shear stress must not exceed 70 mn/m2.
The diameter d of shaft is 0.319m
The actual maximum shear stress of the shaft is 44.95N/m^2
The angle of twist of the 3-m length shaft is 0.01409 rad
The question is incomplete, here is the complete question:
A solid steel shaft 3 m long is transmitting 12 MW at 400 rev/min. The working conditions
to be satisfied by the shaft are:
• The shaft must not twist more than 0.015 radian on a length of 10 times the diameter, i.e., 10D
• The maximum shear stress must not exceed 70 MN/m2.
If the modulus of rigidity of steel is 60 GN/m2 determine:
(a) The diameter of the shaft required
(b) The actual maximum shear stress and the angle of twist of the 3-m length shaft.
Part a
The diameter of the shaft
We use Torque equation to find diameter d:
[tex]\frac{T}{J} =\frac{G\theta }{L}[/tex]
[tex]\frac{12*10^{6}*60 }{25600d^{4} } =\frac{60*10^{9}*0.015 }{10d}[/tex]
[tex]d^{3} =0.032414[/tex]
d=0.319m
Hence, diameter of shaft d=0.319m
Part b
Actual maximum shear stress Y, and the angle of twist of the 3m length shaft
[tex]Y=\frac{16T}{\pi d^{3} }[/tex]
[tex]Y=\frac{16*286478.90}{\pi *0.319^{3} }[/tex]
[tex]Y=44.95N/m^{2}[/tex]
Angle of the twist
Let angle of twist = [tex]\theta[/tex]
[tex]\theta=\frac{TL}{GJ}[/tex]
[tex]=\frac{286478.90*3}{60*10^{9}(\frac{\pi }{32}(0.019)^{9} }[/tex]
=0.01409rad
Angle of twist=0.01409 rad
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The major advantage to using a bearing installation/removal tool to replace a seal in a housing is that the seal will
A. have its inner edge take all of the insertion force
B. go into the housing much straighter than by manual methods.
C. deform slightly creating a better future seal.
D. go deeper into the housing
Advantage in using bearing installation or a removal tool to replace a seal in housing is that seal will have its inner edge taken all the insertion force. Hence, an option a is correct.
Sealed bearing are preferred due to basic aspects such as no accidental over lubrication, as they do not need lubrication thus save time in labor, On the inner track of bearing, it has no contact to the seal's bearing. Since, contaminants can cause wearing and tearing of the machine thus reduce lifespan since sealed bearing is more closed type it thus no contaminants enter since no lubricant is required.
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Imagine that you are the hiring manager at a corporation like ge, with businesses in the healthcare, renewable energy, and operations data fields. Which basic building block of structure would you use as you scale down on managerial positions and scale up on engineering positions?.
As a hiring manager at GE, who is tasked with using the building blocks that managers can use in constructing an organization, the basic building block of structure I would use as I scale down on managerial positions and scale up on engineering positions is C. designing jobs
What is Management?This refers to the process of taking charge of people or processes in order to achieve a set target or common goal, by maximizing or optimizing the available physical and human resources available.
Hence, we can see that based on the fact that I am a hiring manager for a company that has different facets and businesses and want to scale down on management positions and increase or scale up in the positions that require engineers, it would be important to make use of design jobs.
This would help the engineers to produce more things based on already available designs and option C is the correct answer.
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The complete question is:
as a hiring manager at GE, you are tasked with using the building blocks that managers can use in constructing an organization. which basic building block of structure would you use as you scale down on managerial positions and scale up on engineering positions
a. differentiating among positions
b. distributing authority among jobs
c. designing jobs
d. grouping jobs
Give reasons why it is difficult to accurately quantify the quantum of carbon released from terrestrial ecosystems that are as a result of land-use change.
The reason that makes it is difficult to accurately quantify the quantum of carbon released from terrestrial ecosystems are linked with Sensitivity analysis as well as bias made by gap filling of satellite data.
What is the principal quantum of carbon?
In its ground state, the six electrons of carbon (atomic number 6) in the second row of the periodic table occupy two of its primary energy levels, giving the highest-energy electron a principal quantum number n of 2.
Therefore, note that the act of carrying out Sensitivity analysis is a factor that has hindered the knowledge about the amount of release of carbon in the atmosphere.
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technician a says it is important that a full battery test series be done before trying to test the starter system. technician b says the internal condition of the engine has little effect on the operation of the starting system.
When technician a says it is important that a full battery test series be done before trying to test the starter system, and technician b says the internal condition of the engine has little effect on the operation of the starting system, then only technician a is correct.
Ideally, before testing the starter system, full battery test series is to be completed. The reason for this is that both the performance of starter and battery system is so closely related.
And it should also be replaced if it fails the load test. The operation of the starting system will be influenced by the internal condition of the engine.
Therefore, technician a is right.
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the beam supports a uniform dead load of 0.4k/ft, a live load of 1.5k/ft and a single live concentrated force of 8k. determine (a) the maximum positive moment at c and (b) the maximum positive vertical reaction at b. assume a is a roller and b is a pin.
The maximum positive moment at c is 135k/ft
the maximum positive vertical reaction at b is 27k
Part a
Maximum positive moment at c
For maximum positive moment at C and as per Muller's principle, ILD influence line will be on moment at с, this is calculated using the equation below:
Maximum positive moment at c = [tex](\frac{1}{2} *20*5*(0.4+0.5) )+(5*8)[/tex]
= 135k.ft
Part b
Maximum positive vertical reaction at b
To find this using Muller's principle, we keep dead load throughout the span and consequently keep point load at B
Maximum positive vertical reaction at b = [tex](\frac{1}{2} *20*1*(0.4+1.5))+(1*8)[/tex]
= 27k
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the principal values of a stress tensor t are t1 ¼ 10 mpa; t2 ¼ 10 mpa, and t3 ¼ 30 mpa. if the matrix of the stress is given by ½t ¼ t11 0 0 012 0 2 t33 2 4 3 5 10 mpa; find the values of t11 and t33.
The physical state or characteristics of a material can be described using a tensor, which is a multidimensional array of numerical values. Stress is an easy illustration of a tensor that is pertinent to geophysics. Stress is defined as force per unit area, much way pressure is.
Because it depicts events occurring in two directions at once, stress is a tensor1. An interface with constant y can be pushed along by an x-directed force; this is represented by the symbol xy. The stress tensor is the collection of all such combinations, ij, if we put them all together. The force per unit surface exerted at a surface element perpendicular to the direction j constitutes the i-component of the stress tensor, which is represented by the matrix ij(x,t).
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