The transfer function H(s) for the system is H(s) = 1 / (s+2).
What is the transfer function?The given problem describes a causal Linear Time-Invariant Continuous (LTIC) system with a differential equation of the form y(t) + 2y(t) = x(t).
Part (a) requires determining the transfer function H(s) of the system, which is found by taking the Laplace transform of the differential equation and solving for H(s) in terms of X(s) and Y(s).
Part (b) requires finding the impulse response h(t) of the system, which is the inverse Laplace transform of H(s).
Finally, in part (c), the output y(t) is determined for the given input x(t) = e^(-tu) and initial condition y(0) = 2 using Laplace transform techniques and the previously found transfer function H(s).
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Two sites are being considered for wind power generation. On the first site, the wind blows steadily at 7 m/s for 3000 hours per year. On the second site, the wind blows steadily at 10 m/s for 2000 hours per year. The density of air on the both sites is 1.25 kg/m3 . Assuming the wind power generation is negligible during other times.Calculate the maximum power of wind on each site per unit area, in kW/m2 .
Solution :
Given :
[tex]$V_1 = 7 \ m/s$[/tex]
Operation time, [tex]$T_1$[/tex] = 3000 hours per year
[tex]$V_2 = 10 \ m/s$[/tex]
Operation time, [tex]$T_2$[/tex] = 2000 hours per year
The density, ρ = [tex]$1.25 \ kg/m^3$[/tex]
The wind blows steadily. So, the K.E. = [tex]$(0.5 \dot{m} V^2)$[/tex]
[tex]$= \dot{m} \times 0.5 V^2$[/tex]
The power generation is the time rate of the kinetic energy which can be calculated as follows:
Power = [tex]$\Delta \ \dot{K.E.} = \dot{m} \frac{V^2}{2}$[/tex]
Regarding that [tex]$\dot m \propto V$[/tex]. Then,
Power [tex]$ \propto V^3$[/tex] → Power = constant x [tex]$V^3$[/tex]
Since, [tex]$\rho_a$[/tex] is constant for both the sites and the area is the same as same winf turbine is used.
For the first site,
Power, [tex]$P_1= \text{const.} \times V_1^3$[/tex]
[tex]$P_1 = \text{const.} \times 343 \ W$[/tex]
For the second site,
Power, [tex]$P_2 = \text{const.} \times V_2^3 \ W$[/tex]
[tex]$P_2 = \text{const.} \times 1000 \ W$[/tex]
A group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered portion of the flight and that the rocket landed 16.5 s later. The descent parachute failed to deploy so that the rocket fell freely to the ground after reaching its maximum altitude. Assume that g = 32.2 ft/s2.
Determine
(a) the speed v1 of the rocket at the end of powered flight,
(b) the maximum altitude reached by the rocket.
Answer:
[tex]u = 260.22m/s[/tex]
[tex]S_{max} = 1141.07ft[/tex]
Explanation:
Given
[tex]S_0 = 89.6ft[/tex] --- Initial altitude
[tex]S_{16.5} = 0ft[/tex] -- Altitude after 16.5 seconds
[tex]a = -g = -32.2ft/s^2[/tex] --- Acceleration (It is negative because it is an upward movement i.e. against gravity)
Solving (a): Final Speed of the rocket
To do this, we make use of:
[tex]S = ut + \frac{1}{2}at^2[/tex]
The final altitude after 16.5 seconds is represented as:
[tex]S_{16.5} = S_0 + ut + \frac{1}{2}at^2[/tex]
Substitute the following values:
[tex]S_0 = 89.6ft[/tex] [tex]S_{16.5} = 0ft[/tex] [tex]a = -g = -32.2ft/s^2[/tex] and [tex]t = 16.5[/tex]
So, we have:
[tex]0 = 89.6 + u * 16.5 - \frac{1}{2} * 32.2 * 16.5^2[/tex]
[tex]0 = 89.6 + u * 16.5 - \frac{1}{2} * 8766.45[/tex]
[tex]0 = 89.6 + 16.5u- 4383.225[/tex]
Collect Like Terms
[tex]16.5u = -89.6 +4383.225[/tex]
[tex]16.5u = 4293.625[/tex]
Make u the subject
[tex]u = \frac{4293.625}{16.5}[/tex]
[tex]u = 260.21969697[/tex]
[tex]u = 260.22m/s[/tex]
Solving (b): The maximum height attained
First, we calculate the time taken to attain the maximum height.
Using:
[tex]v=u + at[/tex]
At the maximum height:
[tex]v =0[/tex] --- The final velocity
[tex]u = 260.22m/s[/tex]
[tex]a = -g = -32.2ft/s^2[/tex]
So, we have:
[tex]0 = 260.22 - 32.2t[/tex]
Collect Like Terms
[tex]32.2t = 260.22[/tex]
Make t the subject
[tex]t = \frac{260.22}{ 32.2}[/tex]
[tex]t = 8.08s[/tex]
The maximum height is then calculated as:
[tex]S_{max} = S_0 + ut + \frac{1}{2}at^2[/tex]
This gives:
[tex]S_{max} = 89.6 + 260.22 * 8.08 - \frac{1}{2} * 32.2 * 8.08^2[/tex]
[tex]S_{max} = 89.6 + 260.22 * 8.08 - \frac{1}{2} * 2102.22[/tex]
[tex]S_{max} = 89.6 + 260.22 * 8.08 - 1051.11[/tex]
[tex]S_{max} = 1141.0676[/tex]
[tex]S_{max} = 1141.07ft[/tex]
Hence, the maximum height is 1141.07ft
The driver of the truck has an acceleration of 0.4g as the truck passes over the top A of the hump in the road at constant speed. The radius of curvature of the road at the top of the hump is 98 m, and the center of mass G of the driver (considered a particle) is 2 m above the road. Calculate the speed v of the truck.
Answer:
19.81 m/s
Explanation:
The total acceleration of the truck (a) is due to the centripetal acceleration and as a result of the linear acceleration. Therefore the total acceleration (a) is given by:
[tex]a^2=a_n^2+a_t^2\\\\where\ a_n=centripetal\ acceleration=\frac{v^2}{r},a_t=linear \ acceleration\\\\But\ since\ the \ speed\ is \ constant, the \ linear \ acceleration(a_t)\ would\ be\ 0.\\\\a^2=a_n^2+a_t^2\\\\a^2=a_n^2\\\\a=a_n=\frac{v^2}{r} \\\\v^2=ar\\\\v=\sqrt{ar} \\\\a=0.4g=0.4*9.81,r=98\ m+2\ m=100\ m\\\\v=\sqrt{0.4*9.81*100} \\\\v=19.81\ m/s[/tex]
A cylindrical bar of metal having a diameter of 15.7 mm and a length of 178 mm is deformed elastically in tension with a force of 49100 N. Given that the elastic modulus and Poisson's ratio of the metal are 67.1 GPa and 0.34 respectively, Determine the following:(a) The amount by which this specimen will elongate (in mm) in the direction of the applied stress. The entry field with incorrect answer now contains modified data.(b) The change in diameter of the specimen (in mm). Indicate an increase in diameter with a positive number and a decrease with a negative number.
Answer:
0.6727
-0.02017
Explanation:
diameter = 15.7
l = 178
E =elastic modulus = 67.1 Gpa
poisson ratio = 0.34
p = force = 49100N
first we calculate the area of the cross section
[tex]A=\frac{\pi }{4} d^{2}[/tex]
[tex]A=\frac{\pi }{4} (15.7)^{2} \\A = \frac{774.683}{4} \\[/tex]
A = 193.6mm²
1. Change in directon of the applied stress
[tex]= \frac{pl}{AE}[/tex]
= 49100*178/193.6*67.1*10³
= [tex]=\frac{8739800}{12990560}[/tex]
δl = 0.6727 mm
2. change in diameter of the specimen
equation for poisson distribution =
m = -(δd/d) / (δl/l)
0.34 = (δd/15.7) / (0.6727/178)
0.34 = (-δd * 178) / 15.7 * 0.6727
0.34 = -178δd / 10.56139
we cross multiply
10.56139*0.34 =-178δd
3.5908726 = -178δd
δd = 3.5908726/-178
δd = -0.02017 mm
the change in dimeter has a negative sign. it decreases
Describe how to contribute to
zero/low carbon work outcomes
within the built environment.
Answer:
day if you workout without Zero billing that means you're not sweating. Sweating you're not losing anything that means you have zero outcomes
Explanation:
Lab scale tests performed on a cell broth with a viscosity of 5cP gave a specific cake resistance of 1 x1011 cm/g and a negligible medium resistance. The cake solids (dry basis) per volume of filtrate was 20 g/liter. It is desired to operate a larger rotary vacuum filter (diameter 8 m and length 12 m) at a vacuum pressure of 80 kPA with a cake formation time of 20 s and a cycle time of 60 s. Determine the filtration rate in volumes/hr expected for the rotary vacuum filter.
Answer:
5.118 m^3/hr
Explanation:
Given data:
viscosity of cell broth = 5cP
cake resistance = 1*1011 cm/g
dry basis per volume of filtrate = 20 g/liter
Diameter = 8m , Length = 12m
vacuum pressure = 80 kpa
cake formation time = 20 s
cycle time = 60 s
Determine the filtration rate in volumes/hr expected fir the rotary vacuum filter
attached below is a detailed solution of the question
Hence The filtration rate in volumes/hr expected for the rotary vacuum filter
V' = ( [tex]\frac{60}{20}[/tex] ) * 1706.0670
= 5118.201 liters ≈ 5.118 m^3/hr
A 50-mm cube of the graphite fiber reinforced polymer matrix composite material is subjected to 125-kN uniformly distributed compressive force in the direction 2, which is perpendicular to the fiber direction (direction 1). The cube is constrained against expansion in direction 3. Determine:
a. changes in the 50-mm dimensions.
b. stresses required to provide constraints.
Answer:
hello some parts of your question is missing attached below is the missing part
answer :
A) Determine changes in the 50-mm dimensions
The changes are : 0.006mm compression in y-direction
0.002 mm expansion in x and z directions
B) the stress required are evenly distributed
Explanation:
Given data :
50-mm cube of graphite fiber reinforced polymer matrix
subjected to 125-KN force in direction 2,
direction 2 is perpendicular to fiber direction ( direction 1 ) and cube is constrained against expansion in direction 3
A) Determine changes in the 50-mm dimensions
The changes are : 0.006mm compression in y-direction
0.002 mm expansion in x and z directions
B) the stress required are evenly distributed
attached below is the detailed solution
The pressure less than atmospheric pressure is known as:
Suction pressure
Negative gauge pressure
Vacuum pressure
All of the above
Answer:
answer is option (d) all of the above
what is the distance in term of wavelengh between successive minima in the standing wave ratio
Answer:
hi there
Explanation:
If the hypotenuse of a right triangle is 12 and an acute angle is 37 degrees find leg a and leg b lengths
scrity añao devid codicie
Where is the primary area for romanesque architectural sculpture?
Answer:
on the façade, entrance, and column capitals
The demand schedules for Jones, Smith, and other buyers are shown in the table below:
Draw the 4 demand curves for i) Jones ii) Smith iii) Other buyers and iv) All buyers.
The demand curve is the graphical representation of the relationship between the price of a good and the quantity demanded for a given period of time.
What is a demand schedule?A demand schedule is a table which shows the quantity demanded of a good or service at different price levels.
A demand schedule can be graphed as a continuous demand curve on a chart where the Y-axis represents the price and the X-axis represents quantity.
Here, a typical representation, the price will appear on the left vertical axis, the quantity demanded on the horizontal axis.
Note that the complete information wasn't found and an overview was given.
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What are the top 4 solar inventions, how they are used, and how they are better than the original way of powering them
I don’t know the answer to this question
Answer:
I dont know the answer either
Explanation:
Answer:
flux
Explanation:
The need for extraction of raw metals for making steel has been reduced due to the?
Answer: Increase in minimills
Explanation:
Tech A says that LED brake lights illuminate faster than incandescent bulbs. Tech B says that LED brake lights have
more visibility and last longer. Who is correct?
Answer:
Both
Explanation:
What current works best when the operator
encounters magnetic arc blow?
•DCEP
•ACEN
•CC
•AC
Answer:
AC
Explanation:
One situation when alternating current would work better than direct current is if the operator is encountering magnetic arc blow.
Current works best when the operator encounters magnetic arc blow is AC
Magnetic arc blow is simply defined as the arc deflection due to the warping of the magnetic field that is produced by electric arc current.
This is caused as a result of the following;
- if the material being welded has residual magnetism at an intolerable level
- When the weld root is being made, and the welding current is direct current which indicates constant direction and maintains constant polarity (either positive or negative).
Since it is caused by DC(Direct Current) which means constant polarity , it means the opposite will be better which is AC(alternating current) because it means that electricity direction will be switching to and fro and as such the polarity will also be revered in response to this back and forth switch manner.Thus, Current works best when the operator encounters magnetic arc blow is AC
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An example of a power consuming device would be a(n) ____ while an example of a non-power consuming device would be a(n) ____.
An example of a power consuming device would be a(n) light bulb, a computer device while an example of a non-power consuming device would be a(n) switch or button.
What is power consumption?The quantity of energy utilized per unit of time is known as power consumption. Power use is a significant factor in digital systems.
Power consumption is a limiting factor for the battery life of portable devices like laptop computers and cell phones.
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Airtight plugs are installed in the ends of large sizes of PVC conduit during bending to_____________.
Airtight plugs are installed in the ends of large sizes of PVC conduit before bending to A. prevent the conduit from collapsing when heated.
What is Airtight plugs?Airtight plugs is necessary in the PVC conduit so as to be able to avoid the collapse of conduit.
In this case, Airtight plugs are installed in the ends of large sizes of PVC conduit before bending to A. prevent the conduit from collapsing when heated.
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Which of the following choices accurately contrasts a categorical syllogism with a conditional syllogism?
An argument constructed as a categorical syllogism uses deductive reasoning whereas an argument constructed as a conditional syllogism uses inductive reasoning.
A categorical syllogism contains two premise statements and one conclusion whereas a conditional syllogism contains one premise statement and one conclusion.
A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
An argument constructed as a categorical syllogism is valid whereas an argument constructed as a conditional syllogism is invalid.
Answer:
The correct option is - A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
Explanation:
As,
Categorical syllogisms follow an "If A is part of C, then B is part of C" logic.
Conditional syllogisms follow an "If A is true, then B is true" pattern of logic.
So,
The correct option is - A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
I have an AC waveform with the voltage peak value of 100 V. I'm trying to find the RMS value of the voltage
Answer:
98 x 100=9,00
Explanation:
A sign structure on the NJ Turnpike is to be designed to resist a wind force that produces a moment of 25 k-ft in one direction. The axial load is 30 kips. Soil conditions consist of a normally consolidated clay layer with following properties; su=800 psf, andγsat= 110 pcf. Design for a FOS of 3. Assume frost depth to be 3ft below grade
Solution :
Finding the cohesion of the soil(c) using the relation:
[tex]$c = \frac{q_u}{2}$[/tex]
Here, [tex]$q_u$[/tex] is the unconfined compression strength of the soil;
[tex]$c = \frac{800}{2}$[/tex]
= 400 psf
∴ The cohesion value is greater than 0
So the use of the angle of internal friction is 0
Referring to the table relation between bearing capacity factors and angle of internal friction.
For the angle of inter friction [tex]$0^\circ$[/tex]
[tex]$N_c = 5.14$[/tex]
[tex]$N_q = 1.0$[/tex]
[tex]$N_r = 0$[/tex]
Therefore,
[tex]$q_{ult} = (400 \times 5.14 )+(110 \times 3 \times 1.0)+(0.5 \times 100 \times 13 \times 0)$[/tex]
= 2386 psf
∴ Allowable bearing capacity [tex]$q_{a} = \frac{Q_{allow}}{A}$[/tex]
[tex]$=\frac{30}{B^2}$[/tex]
∴ [tex]$q_a = \frac{q_{ult}}{F.O.S}$[/tex]
[tex]$\frac{30}{B^2} = \frac{2386}{3}$[/tex]
∴ B = 0.2 ft
Therefore, the dimension of the square footing is 0.2 ft x 0.2 ft
[tex]$=0.04 \ ft^2$[/tex]
With _____, only one criterion must evaluate true in order for a record to be selected and with _____, all criteria must be evaluate true in order for a record to be selected.
a. parameter criteria, double criteria
b. function criteria, IF criteria
c. simple criteria, complex criteria
d. OR criteria, AND criteria
Answer:
d
Explanation:
OR criteria, AND criteria
In an OR criteria, it doesn't need all the records to be true. Just one record is enough and all other criterion becomes true.
In an AND criteria, it's unlike the OR criteria and works in opposite. It needs every member of the record to be true to be able to adjudge the whole record as true.
And as such, we have
With OR criteria, only one criterion must evaluate true in order for a record to be selected and with AND criteria, all criteria must be evaluate true in order for a record to be selected.
This is silence I couldent find the tab... 30 points plus marked brainliest if corrects!
The most recent evidence supporting the theory of plate tectonics would include
es )
A)
GPS monitoring of plate speeds and movements.
B)
the WWII discovery of paleomagnetic reversals.
Elimi
O
the 1963 mapping of the tectonic plate boundaries.
D
C-14 dating of marine fossils found in the Himalayas.
how skateboards works?
Answer
The skateboarder applies pressure to the trucks and gives/releases pressure on the levers. Second, the wheels and the axles are also examples of simple machines. They help the skater ride, spin, grind, and do a bunch of other radical movements on a skateboard.:
Explanation:
What frequency bands are used primarily for short range distances select all the nearby?
The frequency bands that are used primarily for short-range distances include the following:
The upper portion of the VHF band (225 MHz to 300 MHz).The lower portion of the UHF band (300 MHz to 400 MHz).What is GSM?GSM is an abbreviation for global system for mobile communication and it can be defined as an open and digital cellular network technology that is designed and developed to be used for the transmission of both mobile voice and data services at the same time.
In Computer technology and networking, the global system for mobile communication (GSM) is typically designed and developed to operates at the following bands of frequencies:
850 MHz900 MHz1800 MHz1900 MHzIn this context, we can infer and logically deduce that the frequency bands that are used primarily for short-range distances such as PAN, include the following:
The upper portion of the VHF band (225 MHz to 300 MHz).The lower portion of the UHF band (300 MHz to 400 MHz).Read more on frequency bands here: https://brainly.com/question/19097094
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An isolated pretimed signalized intersection has an approach with a traffic flow rate of 750 veh/h and a saturation flow rate of 3200 veh/h. This approach is allocated 32 seconds of effective green time. The cycle length is 100 seconds. Determine the average approach delay a) 4,6 s b) 30.2 s c) 34.8 s d) 35.0 s
Answer: This approach is allocated 32 seconds of effective green time. The cycle length is 100 seconds. Determine the average approach delay (using Eq. 7.27). A) 34.8 s.
Check Your Understanding: True Stress and Stress A cylindrical specimen of a metal alloy 47.7 mm long and 9.72 mm in diameter is stressed in tension. A true stress of 399 MPa causes the specimen to plastically elongate to a length of 54.4 mm. If it is known that the strain-hardening exponent for this alloy is 0.2, calculate the true stress (in MPa) necessary to plastically elongate a specimen of this same material from a length of 47.7 mm to a length of 57.8 mm.
Answer:
The answer is "583.042533 MPa".
Explanation:
Solve the following for the real state strain 1:
[tex]\varepsilon_{T}=\In \frac{I_{il}}{I_{01}}[/tex]
Solve the following for the real stress and pressure for the stable.[tex]\sigma_{r1}=K(\varepsilon_{r1})^{n}[/tex]
[tex]K=\frac{\sigma_{r1}}{[\In \frac{I_{il}}{I_{01}}]^n}[/tex]
Solve the following for the true state stress and stress2.
[tex]\sigma_{r2}=K(\varepsilon_{r2})^n[/tex]
[tex]=\frac{\sigma_{r1}}{[\In \frac{I_{il}}{I_{01}}]^n} \times [\In \frac{I_{i2}}{I_{02}}]^n\\\\=\frac{399 \ MPa}{[In \frac{54.4}{47.7}]^{0.2}} \times [In \frac{57.8}{47.7}]^{0.2}\\\\ =\frac{399 \ MPa}{[ In (1.14046122)]^{0.2}} \times [In (1.21174004)]^{0.2}\\\\ =\frac{399 \ MPa}{[ In (1.02663509)]} \times [In 1.03915873]\\\\=\frac{399 \ MPa}{0.0114161042} \times 0.0166818905\\\\= 399 \ MPa \times 1.46125948\\\\=583.042533\ \ MPa[/tex]
who was part of dempwolf his firm when he first started
Explanation:
Dempwolf created by John Augustus, Among the most prominent innovative solutions in Southern California Pennsylvania was established by Dempwolf with brother Reinhardt or uncle's son Frederick entered the company of J.A. Dozens of structures in 10 states were engineered by Dempwolf.
Find the derivative of x
Answer:
this is your answer. if mistake don't mind.