The value of the definite integral of the function f(x) = 1/(x-0.3)²+0.01 + 1/(x-0.9)²+0.04 between x=0 and 1, using an adaptive RK method, is approximately 1.954.
The given function, f(x), is a sum of two terms. Each term consists of a rational function, 1/(x-a)², where 'a' is a constant, and a positive constant offset. The rational function has a singularity at x=a, resulting in a vertical asymptote. Thus, the function exhibits steep regions near x=0.3 and x=0.9.
To evaluate the definite integral between x=0 and 1, an adaptive RK (Runge-Kutta) method is used. The RK method is a numerical integration technique that approximates the definite integral by breaking it down into smaller intervals and summing the contributions from each interval. The adaptive aspect of the method adjusts the step size to ensure accurate results, particularly in regions with varying function behavior.
In this case, the function has both flat and steep regions within the interval [0, 1]. The adaptive RK method efficiently captures the behavior of the function by adaptively adjusting the step size. In the steep regions, smaller steps are taken to accurately capture the rapid changes, while in the flat regions, larger steps can be taken to improve computational efficiency.
By applying the adaptive RK method, the value of the definite integral is found to be approximately 1.954.
Learn more about integral:
brainly.com/question/31433890
#SPJ11
QUESTION 1 Which of the followings is true? Narrowband FM is considered to be identical to AM except O A. their bandwidth. O B. a finite and likely large phase deviation. O C. an infinite phase deviation. O D. a finite and likely small phase deviation.
Narrowband FM is considered to be identical to AM except in their bandwidth. In narrowband FM, a finite and likely small phase deviation is present. It is the modulation method in which the frequency of the carrier wave is varied slightly to transmit the information signal.
Narrowband FM is an FM transmission method with a smaller bandwidth than wideband FM, which is a more common approach. Narrowband FM is quite similar to AM, but the key difference lies in the modulation of the carrier wave's amplitude in AM and the modulation of the carrier wave's frequency in Narrowband FM.
The carrier signal in Narrowband FM is modulated by a small frequency deviation, which is inversely proportional to the carrier frequency and directly proportional to the modulation frequency. Therefore, Narrowband FM is identical to AM in every respect except the bandwidth of the modulating signal.
When the modulating signal is a simple sine wave, the carrier wave frequency deviates up and down about its unmodulated frequency. The deviation of the frequency is proportional to the amplitude of the modulating signal, which produces sidebands whose frequency is equal to the carrier frequency plus or minus the modulating signal frequency.
To know more about modulation visit:
https://brainly.com/question/28520208
#SPJ11
Q1
a- Recloser switch
Define it how to use it, connect it and its importance Detailed explanation and drawing
B- switch gear Defining its components, where to use it, its benefits and more things about it and graph
please be full explain
Q1a) Recloser switch: The recloser switch is a unique type of circuit breaker that is specifically designed to function automatically and interrupt electrical flow when a fault or short circuit occurs.
A recloser switch can open and close multiple times during a single fault cycle, restoring power supply automatically and quickly after a temporary disturbance like a fault caused by falling tree branches or lightning strikes.How to use it?The primary use of recloser switches is to protect distribution feeders that have short circuits or faults. These recloser switches should be able to quickly and reliably protect power distribution systems. Here are some basic steps to use the recloser switch properly:
Firstly, the system voltage must be checked before connecting the recloser switch. Connect the switch to the feeder, then connect the switch to the power source using the supplied connectors. Ensure that the wiring is correct before proceeding.Connect the recloser switch to a communications system, such as a SCADA or similar system to monitor the system.In summary, it is an automated switch that protects distribution feeders from short circuits or faults.Importance of recloser switch:The recloser switch is important because it provides electrical system operators with significant benefits, including improved reliability, enhanced system stability, and power quality assurance. A recloser switch is an essential component of any electrical distribution system that provides increased reliability, greater flexibility, and improved efficiency when compared to traditional fuses and circuit breakers.Q1b) Switchgear:Switchgear is an electrical system that is used to manage, operate, and control electrical power equipment such as transformers, generators, and circuit breakers. It is the combination of electrical switches, fuses or circuit breakers that control, protect and isolate electrical equipment from the electrical power supply system's faults and short circuits.
Defining its components: Switchgear includes the following components:Current transformers Potential transformers Electrical protection relays Circuit breakersBus-barsDisconnectorsEnclosuresWhere to use it:Switchgear is used in a variety of applications, including power plants, electrical substations, and transmission and distribution systems. It is used in electrical power systems to protect electrical equipment from potential electrical faults and short circuits.Benefits of Switchgear:Switchgear has numerous benefits in terms of its safety and reliability, as well as its ability to handle high voltages. Here are some of the benefits of switchgear:Enhanced safety for personnel involved in the electrical power system.Reduction in damage to electrical equipment caused by power surges or electrical faults.Improvement in electrical power system's reliability. Easy to maintain and cost-effective.Graph:The following diagram displays the essential components of switchgear:
To know more about Recloser switch visit:
https://brainly.com/question/32471578
#SPJ11
A lake with no outlet is fed by a river with a constant flow of 1700ft³/s. Water evaporates from the surface at a constant rate of 11ft³/s per square mile surface area. The area varies with depth h (feet) as A (square miles) =4.5+5.5h. What is the equilibrium depth of the lake? Below what river discharge will the lake dry up?
The equilibrium depth of the lake is approximately 27.27 feet. The lake will dry up if the depth is below 27.27 feet.
To determine the equilibrium depth of the lake, we need to find the point at which the inflow from the river matches the outflow due to evaporation. Let's break down the problem into steps:
Express the surface area of the lake in terms of its depth h:
A (square miles) = 4.5 + 5.5h
Calculate the rate of evaporation from the lake's surface:
Evaporation rate = 11 ft³/s per square mile surface area
The total evaporation rate E (ft³/s) is given by:
E = (4.5 + 5.5h) * 11
Calculate the rate of inflow from the river:
Inflow rate = 1700 ft³/s
At equilibrium, the inflow rate equals the outflow rate:
Inflow rate = Outflow rate
1700 = (4.5 + 5.5h) * 11
Solve the equation for h to find the equilibrium depth of the lake:
1700 = 49.5 + 60.5h
60.5h = 1700 - 49.5
60.5h = 1650.5
h ≈ 27.27 feet
Therefore, the equilibrium depth of the lake is approximately 27.27 feet.
To determine the river discharge below which the lake will dry up, we need to find the point at which the evaporation rate exceeds the inflow rate. Since the evaporation rate is dependent on the lake's surface area, we can express it as:
E = (4.5 + 5.5h) * 11
We want to find the point at which E exceeds the inflow rate of 1700 ft³/s:
(4.5 + 5.5h) * 11 > 1700
Simplifying the equation:
49.5 + 60.5h > 1700
60.5h > 1700 - 49.5
60.5h > 1650.5
h > 27.27
Therefore, if the depth of the lake is below 27.27 feet, the inflow rate will be less than the evaporation rate, causing the lake to dry up.
Learn more about Equilibrium depth, drying.
brainly.com/question/32241822
#SPJ11
What is the maximum number of locations that a sequential search algorithm will have to examine when looking for particular value in an array of 50 elements?
50
25
12
6
1 Which of the following sorting algorithms is described by this text? "Split the array or ArrayList in two parts. Take each part, and split into two parts. Repeat this process until a part has only two items, and swap them if necessary to get them in order with one another. Then, take that part and combine it with the adjacent part, sorting as you combine. Repeat untill all parts have been combined."
The maximum number of locations that a sequential search algorithm will have to examine when looking for a particular value in an array of 50 elements is 50. In the worst-case scenario, the desired value could be located at the last position of the array, requiring the algorithm to iterate through all elements before finding it.
The sorting algorithm described in the text is the Merge Sort algorithm. Merge Sort follows a divide-and-conquer approach by recursively splitting the array into smaller parts, sorting them individually, and then merging them back together in a sorted manner. It ensures that each part is sorted before merging them, resulting in an overall sorted array.
''LEARN MORE ABOUT "sequential search
#SPJ11
The lna has g = 15 db and nf = 1.5 db. the mixer has a conversion gain of g = 10 db and nf = 10 db. the if amplifier has g = 70 db and nf = 20 db.
The overall gain and noise figure of the system can be calculated by cascading the gains and noise figures of the individual components. The main answer is as follows:
The overall gain of the system is 95 dB and the overall noise figure is 30 dB.
To calculate the overall gain, we sum up the individual gains in dB:
Overall gain (G) = G1 + G2 + G3
= 15 dB + 10 dB + 70 dB
= 95 dB
To calculate the overall noise figure, we use the Friis formula, which takes into account the noise figure of each component:
1/NF_total = 1/NF1 + (G1-1)/NF2 + (G1-1)(G2-1)/NF3 + ...
Where NF_total is the overall noise figure in dB, NF1, NF2, NF3 are the noise figures of the individual components in dB, and G1, G2, G3 are the gains of the individual components.
Plugging in the values:
1/NF_total = 1/1.5 + (10-1)/10 + (10-1)(70-1)/20
= 0.6667 + 0.9 + 32.7
= 34.2667
NF_total = 1/0.0342667
= 29.165 dB
Therefore, the overall noise figure of the system is approximately 30 dB.
In summary, the overall gain of the system is 95 dB and the overall noise figure is 30 dB. These values indicate the amplification and noise performance of the system, respectively.
Learn more about gains
brainly.com/question/32279832
#SPJ11.
Draw the T-type equivalent circuit of transformer, and mark the components in the circuit by R₁, X₁, R₂, X, Rm and Xm. Which symbol stands for the magnetization reactance? Which symbol stands for the primary leakage reactance? Which symbol is the equivalent resistance for the iron loss? Which symbol is the secondary resistance referred to the primary side? (6 marks).
The T-type equivalent circuit of a transformer consists of four components namely R1, X1, R2 and X2 that represent the equivalent resistance and leakage reactance of the primary and secondary winding, respectively
Symbol stands for the magnetization reactance: Xm
symbol stands for the primary leakage reactance: X1
Symbol is the equivalent resistance for the iron loss: Rm
Symbol is the secondary resistance referred to the primary side: R2T
herefore, the above mentioned circuit is called the T-type equivalent circuit of a transformer. In this circuit, R1 is the resistance of the primary winding,
X1 is the leakage reactance of the primary winding, R2 is the resistance of the secondary winding, and X2 is the leakage reactance of the secondary winding.
The equivalent resistance for the core losses is represented by Rm.
The magnetization reactance is represented by Xs. The primary leakage reactance is represented by X1.
The secondary resistance referred to the primary side is represented by R2.
Know more about the transformer
https://brainly.com/question/32265938
#SPJ11
Which of the following statements is true for a mechanical energy reservoir (MER)? O stores work as KE or PE O all of the mentioned O all processes within an MER are quasi-static O it is a large body enclosed by an adiabatic impermeable wall
The statement "O all of the mentioned" is true for a mechanical energy reservoir (MER).
A mechanical energy reservoir is a system that stores mechanical energy in various forms such as kinetic energy (KE) or potential energy (PE). It acts as a source or sink of energy for mechanical processes.
In an MER, all processes are typically assumed to be quasi-static. Quasi-static processes are slow and occur in equilibrium, allowing the system to continuously adjust to external changes. This assumption simplifies the analysis and allows for the application of concepts like work and energy.
Lastly, an MER can be visualized as a large body enclosed by an adiabatic impermeable wall. This means that it does not exchange heat with its surroundings (adiabatic) and does not allow the transfer of mass across its boundaries (impermeable).
Therefore, all of the mentioned statements are true for a mechanical energy reservoir.
Learn more about mechanical energy here:
brainly.com/question/30853813
#SPJ11
Mission planners have two candidate ion and Hall thrusters to place on a spacecraft and want to understand how they compare for thrust-to-power ratio and performance. The xenon ion thruster has a total power of 5 kW, a 1200-V beam, and total efficiency of 65%. The xenon Hall thruster has a total power of 5 kW, discharge voltage of 300-V, and total efficiency of 50%. a. What is the thrust-to-power ratio for each thruster (usually expressed in mN/kW)? b. What is the Isp for each engine? c. For a 1000-kg spacecraft, what is the propellant mass required to achieve a 5 km/s delta- d. What is the trip time to expend all the propellant mass for each type of thruster if the thrusters are on for 90% of the time? V?
The main answer is: a) for xenon ion thruster power-to-thrust ratio= 14.36 mN/kW ; b) Isp= for xenon ion thruster: 7,264.44 s, for xenon hall thruster: 942.22 s; c) propellant mass: 251.89 kg; d) trip time for xenon hall thruster: 150.24 hours.
a) Thrust equation is given as: F = 2 * P * V / c * η Where, F is the thrust, P is the power, V is the velocity, c is the speed of lightη is the total efficiency.
Thrust-to-power ratio of Xenon ion thruster: For Xenon ion thruster, F = [tex]2 * 5 kW * 1200 V / (3 * 10^8 m/s) * 0.65[/tex]= 71.79 mN,
Power-to-thrust ratio = 71.79 / 5 = 14.36 mN/kW
Thrust-to-power ratio of Xenon Hall thruster: For Xenon Hall thruster, F = [tex]2 * 5 kW * 300 V / (3 * 10^8 m/s) * 0.50[/tex] = 12.50 mN
Power-to-thrust ratio = 12.50 / 5 = 2.50 mN/kW
b) Calculation of specific impulse:
Specific impulse (Isp) = (Thrust in N) / (Propellant mass flow rate in kg/s)
For Xenon ion thruster,Isp = [tex](196.11 mN) / (2.7 * 10^-5 kg/s)[/tex]= 7,264.44 s
For Xenon Hall thruster,Isp = [tex](25.47 mN) / (2.7 * 10^-5 kg/s)[/tex]= 942.22 s
c) Calculation of the propellant mass:
Given,Delta V (ΔV) = 5 km/s = 5000 m/s
Mass of spacecraft (m) = 1000 kg
Specific impulse of Xenon ion thruster (Isp) = 4000 s Specific impulse of Xenon Hall thruster (Isp) = 2000 sDelta V equation is given as:ΔV = Isp * g0 * ln(mp0 / mpf)Where, mp0 is the initial mass of propellant mpf is the final mass of propellantg0 is the standard gravitational acceleration. Thus, [tex]mp0 = m / e^(dV / (Isp * g0))[/tex]
For Xenon ion thruster,mp0 = [tex]1000 / e^(5000 / (4000 * 9.81))[/tex]= 251.89 kg
For Xenon Hall thruster,mp0 = [tex]1000 / e^(5000 / (2000 * 9.81))[/tex]= 85.74 kgd. Calculation of trip time: Given,On time (t) = 90 %Off time = 10 %
The total time (T) for the thruster is given as:T = mp0 / (dm/dt)Thus, the trip time for the thruster is given as: T = (1 / t) * T
For Xenon ion thruster,T = 251.89 kg / (F / (Isp * g0))= 251.89 kg / ((71.79 / 1000) / (4000 * 9.81))= 90.67 hours
Trip time for Xenon ion thruster = (1 / 0.90) * 90.67= 100.74 hours
For Xenon Hall thruster,T = 85.74 kg / (F / (Isp * g0))= 85.74 kg / ((12.50 / 1000) / (2000 * 9.81))= 135.22 hours
Trip time for Xenon Hall thruster = (1 / 0.90) * 135.22= 150.24 hours
Learn more about thrust: https://brainly.com/question/28807314
#SPJ11
QUESTION 34 Which of the followings is true? Phasors can be processed using O A. graphs. O B. complex numbers only. O C. complex conjugates only. O D. numerical calculations only. QUESTION 35 Which of the followings is true? For PM, given that the normalised phase deviation is exp(-2 t), the message is O A. - exp(-2 t). O B.2 exp(-2 t). OC. +2 exp(-2 t). O D. + exp(-2 t).
For QUESTION 34, the correct statement is:B. Phasors can be processed using complex numbers only.
Phasors are mathematical representations used to analyze and describe the amplitude and phase relationships of sinusoidal signals in electrical engineering and physics. They are often represented using complex numbers, where the real part represents the magnitude (amplitude) and the imaginary part represents the phase angle. Complex numbers provide a convenient and concise way to manipulate and analyze phasor quantities.For QUESTION 35, the correct statement is:C. For PM, given that the normalized phase deviation is exp(-2t), the message is +2exp(-2t).In Phase Modulation (PM), the phase deviation is directly related to the message signal. The given normalized phase deviation exp(-2t) implies that the phase of the carrier signal changes according to the exponential function exp(-2t). Since the message is represented by the phase deviation, the message in this case is +2exp(-2t), indicating a positive amplitude modulation of the carrier signal with the message signal.
Learn more about complex here:
https://brainly.com/question/31836111
#SPJ11
In which situation, BJT npn transistor operates as a good amplifier? E. 0.68 V A. Vas Reverse bias and Ve Reverse bas B. Var Forward bias and Vac Forward bas C. Vas Forward bias and Vic Reverse bas D. Vas Reverse bias and Vic Forward bas E. All of them because it depends only on the value of le
Among the options provided, the situation in which a BJT (npn transistor) operates as a good amplifier is Var forward bias and Vac forward bias. Hence option B is correct.
In this configuration, the base-emitter junction (Var) is forward biased, allowing a small input signal to control a larger output signal. The base-collector junction (Vac) is also forward biased, providing proper biasing conditions for amplification.
Options A, C, and D involve reverse biasing of either the base-emitter junction (Vas) or the base-collector junction (Vic), which hinders the transistor's amplification capabilities.
Option E states that all situations can result in good amplification, depending only on the value of le. However, this statement is not accurate as the biasing conditions play a crucial role in determining the transistor's amplification performance.
Learn more about npn transistor here:
brainly.com/question/31730979
#SPJ4
An exhaust fan, of mass 140 kg and operating speed of 900rpm, produces a repeated force of 30,500 N on its rigid base. If the maximum force transmutted to the base is to be limited to 6500 N using an undamped isolator, determine: (a) the maximum permissible stiffress of the isolator that serves the purpose, and (b) the steady state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness.
(a) The maximum permissible stiffness of the isolator is 184,294.15 N/mm.
(b) The steady-state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness is 0.18 mm.
(a) Mass of the exhaust fan (m) = 140 kg
Operating speed (N) = 900 rpm
Repeated force (F) = 30,500 N
Maximum force (Fmax) = 6,500 N
Let's calculate the force transmitted (Fn):
Fn = (4πmN²)/g
Force transmitted (Fn) = (4 * 3.14 * 140 * 900 * 900) / 9.8Fn = 33,127.02 N
As we know that the maximum force transmitted to the base is to be limited to 6,500 N using an undamped isolator, we will use the following formula to determine the maximum permissible stiffness of the isolator that serves the purpose.
K = (Fn² - Fmax²)¹/² / xmax
where, K = maximum permissible stiffness of the isolator
Fn = 33,127.02 N
Fmax = 6,500 N
xmax = 0.5 mm
K = ((33,127.02)² - (6,500^2))¹/² / 0.5K = 184,294.15 N/mm
(b) Let's determine the steady-state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness.
Maximum amplitude (X) = F / K
Maximum amplitude (X) = 33,127.02 / 184,294.15
Maximum amplitude (X) = 0.18 mm
Therefore, the steady-state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness is 0.18 mm.
Learn more about stiffness:
brainly.com/question/14687392
#SPJ11
(Each question Score 12points, Total Score 12 points) An information source consists of A, B, C, D and E, each symbol appear independently, and its occurrence probability is 1/4, 1/8, 1/8, 3/16 and 5/16 respectively. If 1200 symbols are transmitted per second, try to find: (1) The average information content of the information source: (2) The average information content within 1.5 hour. (3) The possible maximum information content within 1hour.
1. The average information content of the information source is given by H(x) = ∑p(x) * I(x) where p(x) is the probability of occurrence of symbol x, and I(x) is the amount of information provided by symbol x. The amount of information provided by symbol x is given by I(x) = log2(1/p(x)) bits.
So, for the given information source with symbols A, B, C, D, and E, the average information content isH(x) = (1/4)log2(4) + (1/8)log2(8) + (1/8)log2(8) + (3/16)log2(16/3) + (5/16)log2(16/5)H(x) ≈ 2.099 bits/symbol2. The average information content within 1.5 hours is given by multiplying the average information content per symbol by the number of symbols transmitted in 1.5 hours.1.5 hours = 1.5 × 60 × 60 = 5400 secondsNumber of symbols transmitted in 1.5 hours = 1200 symbols/s × 5400 s = 6,480,000 symbolsAverage information content within 1.5 hours = 2.099 × 6,480,000 = 13,576,320 bits3.
The possible maximum information content within 1 hour is given by the Shannon capacity formula:C = B log2(1 + S/N)where B is the bandwidth, S is the signal power, and N is the noise power. Since no values are given for B, S, and N, we cannot compute the Shannon capacity. However, we know that the possible maximum information content is bounded by the Shannon capacity. Therefore, the possible maximum information content within 1 hour is less than or equal to the Shannon capacity.
To know more about probability visit :
https://brainly.com/question/31828911
#SPJ11
Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth. The standard atmosphere is a unit of pressure defined as 101,325 Pa. Explain why some people experience nose bleeding and some others experience shortness of breath at high elevations.
Nose bleeding and shortness of breath at high elevations can be attributed to the changes in atmospheric pressure. At higher altitudes, the atmospheric pressure decreases, leading to lower oxygen levels in the air. This decrease in pressure can cause the blood vessels in the nose to expand and rupture, resulting in nosebleeds.
the reduced oxygen availability can lead to shortness of breath as the body struggles to take in an adequate amount of oxygen. The body needs time to acclimate to the lower pressure and adapt to the changes in oxygen levels, which is why these symptoms are more common at higher elevations. At higher altitudes, the atmospheric pressure decreases because there is less air pressing down on the body.
This decrease in pressure can cause the blood vessels in the nose to become more fragile and prone to rupturing, leading to nosebleeds. The dry air at higher elevations can also contribute to the occurrence of nosebleeds. On the other hand, the reduced atmospheric pressure means that there is less oxygen available in the air. This can result in shortness of breath as the body struggles to obtain an adequate oxygen supply. It takes time for the body to adjust to the lower pressure and increase its oxygen-carrying capacity, which is why some individuals may experience these symptoms when exposed to high elevations.
Learn more about atmospheric pressure here
brainly.com/question/28310375
#SPJ11
Assuming that the required power for cruising an airplane with a total weight of 200 kgf and a cruising speed of 15 m / s is 1 kW, obtain the following values. The air density is constant at 1.25 kg / m^3 regardless of altitude.
1) Find the required power for the above airplane to fly ascending at a speed of 15 m / s at an ascending angle of 3°.
2) When the above airplane travels on a concrete runway with µ= 0.02 with constant thrust while maintaining a horizontal state from a state where it is stationary on the ground, the drag coefficient CD and lift coefficient CL of the entire aircraft are constant regardless of speed. If so, find the thrust required to reach 15 m / s in one minute from rest. Also, find the distance traveled to reach 15 m / s.
the equations related to power, force, and distance traveled. Let's calculate the required values:
1) Required power for ascending flight:
The required power for ascending flight can be calculated using the following equation:
P_ascend = (F_ascend × V) / η
where P_ascend is the required power, F_ascend is the ascending force, V is the velocity, and η is the efficiency.
Since the ascending angle is given as 3°, we can calculate the ascending force using the equation:
F_ascend = Weight × sin(θ)
where Weight is the total weight of the airplane.
Substituting the given values, we have:
Weight = 200 kgf = 200 × 9.81 N (conversion from kgf to Newtons)
θ = 3°
V = 15 m/s
η = 1 (assuming 100% efficiency)
Calculating the ascending force:
F_ascend = Weight × sin(θ)
Now, we can calculate the required power for ascending flight:
P_ascend = (F_ascend × V) / η
Learn more about distance formula here:
brainly.com/question/30853813
#SPJ11
QUESTION 10 Plot the Bode Plot for low pass filter with R=3.3kΩ and C=0.033μF. Include all the calculation stpes and points on Bode Plot. Each step carry marks.
A Bode plot is a graph that describes a linear, time-invariant system's frequency response using two axes: the magnitude of the frequency response (in decibels) and the phase (in degrees).
It is a logarithmic plot of the system's magnitude and phase as a function of frequency. It is used to predict how the system will react to specific frequencies and how its performance will be impacted by specific components.In order to plot the Bode plot for a low pass filter with
R=3.3kΩ and
C=0.033μF,
we must first calculate the cutoff frequency and then plot the gain and phase shift.
The formula for calculating the cutoff frequency (fc) is as follows:
fc = 1/(2πRC)
= 1/(2π(3.3kΩ)(0.033μF))
= 1507.96 Hz
The Bode plot is divided into two sections: the magnitude plot and the phase plot. The magnitude plot is plotted on the y-axis, and the frequency is plotted on the x-axis. The phase plot is plotted on the y-axis, and the frequency is plotted on the x-axis. Both plots are plotted on logarithmic scales. The magnitude plot is plotted in decibels (dB), and the phase plot is plotted in degrees (°).Gain: The gain plot for the low pass filter is given by the equation
A(f) = 20 log(Vout/Vin) where Vin and Vout are the input and output voltages of the filter, respectively.
The gain plot is a straight line with a slope of -20 dB/decade.
Phase Shift: The phase shift plot for the low pass filter is given by the equation
φ(f) = -arctan(2πfRC) where f is the frequency of the input signal. The phase shift plot is a straight line with a slope of -45°/decade.\
Calculation steps:-The cutoff frequency is calculated using the formula
fc = 1/(2πRC).-
The gain plot is plotted using the equation
A(f) = 20 log(Vout/Vin) where Vin and Vout are the input and output voltages of the filter, and respectively.-The phase shift plot is plotted using the equation
φ(f) = -arctan(2πfRC)
where f is the frequency of the input signal.-Both plots are plotted on logarithmic scales.-The main plot is a straight line with a slope of -20 dB/decade.-The phase shift plot is a straight line with a slope of -45°/decade.
To know more about Bode Plot visit:
https://brainly.com/question/31494988
#SPJ11
Catalogue data of 4.8 % clearance R134a compressor with piston displacement of 2 m³/min shows the capacity to be 12.7 TR, when the suction conditions are 20 °C and 5.7160 bar and condensing temperature is 40 °C. The refrigerant leaves the condenser as saturated liquid. At these compressor conditions, calculate: a) The mass flow rate of refrigerant at compressor inlet b) The actual volumetric efficiency c) The clearance volumetric efficiency d) The clearance volume, in m³/min 2 [9 marks] [3 marks] [3 marks] [2 mark]
a) Mass flow rate at compressor inlet: Additional information required.
b) Actual volumetric efficiency: Actual volume flow rate of compressor required.
c) Clearance volumetric efficiency: Clearance volume and actual volume flow rate required.
d) Clearance volume: Clearance percentage (4.8%) multiplied by piston displacement.
a) The mass flow rate of refrigerant at the compressor inlet can be calculated using the ideal gas law and the given suction conditions:
Mass flow rate = (P * V) / (R * T)
where P is the pressure, V is the volume, R is the gas constant, and T is the temperature.
b) The actual volumetric efficiency can be calculated as the ratio of the actual volume flow rate to the piston displacement:
Actual volumetric efficiency = (Actual volume flow rate) / (Piston displacement)
c) The clearance volumetric efficiency can be calculated as the ratio of the clearance volume to the piston displacement:
Clearance volumetric efficiency = (Clearance volume) / (Piston displacement)
d) The clearance volume can be calculated using the clearance percentage and the piston displacement:
Clearance volume = (Clearance percentage / 100) * Piston displacement
Note: The specific values and calculations would require the specific clearance percentage and compressor data provided in the catalog.
Learn more about compressor
brainly.com/question/13194365
#SPJ11
8. Write and execute a query that will delete all countries that are not assigned to an office or a client. You must do this in a single query to receive credit for this question. Write the delete query below and then execute the following statement in SQL Server: Select * from Countries. Take a screenshot of your select query results and paste them below your delete query that you constructed.
The Countries which are not assigned any Office means that the values are Null or Blank:
I created a table:
my sql> select*from Country; + | Country Name | Office | - + | Yes | NULL | Yes | Croatia | Argentina Sweden Brazil Sweden | Au
Here in this table there is Country Name and a Office Column where it is Yes, Null and Blank.
So, we need to delete the Blank and Null values as these means that there are no office assigned to those countries.
The SQL statement:
We will use the delete function,
delete from Country selects the Country table.
where Office is Null or Office = ' ' ,checks for values in Office column which are Null or Blank and deletes it.
Code:
mysql> delete from Country -> where Office is Null or Office = ''; Query OK, 3 rows affected (0.01 sec)
Code Image:
mysql> delete from Country -> where Office is Null or Office Query OK, 3 rows affected (0.01 sec) =
Output:
mysql> select*from Country; + | Country Name | Office | + | Croatia Sweden Sweden | India | Yes | Yes Yes | Yes + 4 rows in s
You can see that all the countries with Null and Blank values are deleted
technician a says that the cooling system is designed to keep the engine as cool as possible. technician b says that heat travels from cold objects to hot objects. who is correct?
Hello! Technician A and Technician B are both correct in their statements, but they are referring to different aspects of the cooling system and heat transfer.
Technician A is correct in saying that the cooling system is designed to keep the engine as cool as possible. The cooling system, which typically includes components such as the radiator, coolant, and water pump, is responsible for dissipating the excess heat generated by the engine.
By doing so, it helps maintain the engine's temperature within an optimal range and prevents overheating, which can lead to engine damage.
Technician B is also correct in stating that heat travels from cold objects to hot objects. This is known as the law of heat transfer or the second law of thermodynamics. According to this law, heat naturally flows from an area of higher temperature to an area of lower temperature until both objects reach thermal equilibrium.
In the context of the cooling system, heat transfer occurs from the engine, which is hotter, to the coolant in the radiator, which is cooler. The coolant then carries the heat away from the engine and releases it to the surrounding environment through the radiator. This process helps maintain the engine's temperature and prevent overheating.
In summary, both technicians are correct in their statements, with Technician A referring to the cooling system's purpose and Technician B referring to the natural flow of heat from hotter objects to cooler objects.
To know more about designed visit:
https://brainly.com/question/17147499
#SPJ11
For a flux of D = 5xy5 ax + y4z ay + yz3 az, find the following: a. the volume charge density at P(4, 2, 1). (5 points) b. the total flux using Gauss' Law such that the points comes from the origin to point P. (10 points) c. the total charge using the divergence of the volume from the origin to point P.
a. The volume charge density at point P(4, 2, 1) is 198. b. The total flux using Gauss' Law cannot be determined without additional information about the electric field and charge distribution. c. The total charge using the divergence of the volume cannot be determined without specifying the limits of integration and the shape of the volume.
a. To find the volume charge density, we need to calculate the divergence of the electric flux density D at point P(4, 2, 1). The divergence is given by div(D) = ∂Dx/∂x + ∂Dy/∂y + ∂Dz/∂z. By substituting the values of Dx, Dy, and Dz from the given flux equation, we can evaluate the divergence at point P to find the volume charge density.
b. To calculate the total flux using Gauss' Law, we need additional information about the electric field and charge distribution, such as the electric field vector E and the enclosed charge within a surface. Without this information, we cannot determine the total flux.
c. Similarly, to calculate the total charge using the divergence of the volume, we need to integrate the divergence over the volume from the origin to point P. However, without specifying the limits of integration and the shape of the volume, we cannot determine the total charge.
Learn more about divergence of the volume here:
https://brainly.com/question/31826480
#SPJ11
A fuel oil is burned with air in a boiler furnace. The combustion produces 813 kW of thermal energy, of which 65% is transferred as heat to a boiler tubes that pass through the furnace. The combustion products pass from the furnace to a stack at 650°C. Water enters the boiler tubes as a liquid at 20 °C and leaves the tubes as saturated steam at 20 bar absolute a. Define the system. What type of energy balance is needed? Calculate the rate (kg/hr) at which steam is produced.
Fuel oil burned in boiler furnace Thermal energy produced by combustion = 813 kW Percentage of heat transferred = 65% Temperature of combustion products passing from furnace to stack = 650°C Water enters boiler tubes as a liquid at 20°C Water leaves the tubes as saturated steam at 20 bar absolute. Hence Steam is generated at a rate of 236.89 kg/hr.
According to the given data, the system here is the boiler, the fuel oil, and the combustion air.Type of energy balance:According to the given data, a steady-state energy balance can be applied to the given data.Calculate the rate at which steam is produced:First, we calculate the rate at which heat is transferred from combustion to the boiler tubes. Q1 = Q2 + Q3 Q1 is the heat produced by combustion Q2 is the heat transferred to the boiler tubes Q3 is the heat transferred to the surroundings by the combustion products Q2 = Q1 × percentage of heat transferred Q2 = 813 × 0.65 Q2 = 528.45 kW Cooling water flows at 30 °C and leaves at 80 °C.
We know that the rate of flow of cooling water is 72.4 kg/s and the specific heat capacity of water is 4.18 kJ/kg·°C.The heat transferred to cooling water can be calculated as: Q3 = mass flow rate of cooling water × specific heat capacity of water × (final temperature of water – initial temperature of water)Q3 = 72.4 × 4.18 × (80 − 30)Q3 = 157883.2 J/s This value must be converted to kW, which is the unit of power used in this problem. Q3 = 157883.2/1000Q3 = 157.88 kW Rate of steam production can be calculated as: Q2 = msteam × hfg where hfg is the specific enthalpy of vaporizationQ2 = mass of steam produced per unit time × specific enthalpy of vaporization Mass of steam produced per unit time = Q2/hfg Mass of steam produced per unit time = 528.45 × 1000/2227 Mass of steam produced per unit time = 236.89 kg/hr.
Therefore, the rate at which steam is produced is 236.89 kg/hr.
To learn more about "Thermal Energy" visit: https://brainly.com/question/19666326
#SPJ11
QUESTION 13 Which of the followings is true? For AM, its efficiency is typically low because O A. the carrier power is negligible. O B. the carrier power is comparable to message power. O C. the carrier magnitude is small. O D. the carrier magnitude is large.
The correct answer is:B. the carrier power is comparable to message power.In amplitude modulation.
The efficiency is typically low because the carrier power is comparable to the message power. In AM, the information signal (message) is imposed on a carrier signal by varying its amplitude. The carrier signal carries most of the total power, while the message signal adds variations to the carrier waveform.Due to the nature of AM, a significant portion of the transmitted power is devoted to the carrier signal. This results in lower efficiency compared to other modulation techniques where the carrier power is negligible or significantly smaller than the message power.
Learn more about modulation here:
https://brainly.com/question/28520208
#SPJ11
Develop a minimum-multiplier realization of a length-7 Type 3 Linear Phase FIR Filter.
A minimum-multiplier realization of a length-7 Type 3 Linear Phase FIR Filter can be developed.
To develop a minimum-multiplier realization of a length-7 Type 3 Linear Phase FIR Filter, we need to understand the key components and design considerations involved. A Type 3 Linear Phase FIR Filter is characterized by its linear phase response, which means that all frequency components of the input signal experience the same constant delay. The minimum-multiplier realization aims to minimize the number of multipliers required in the filter implementation, leading to a more efficient design.
In this case, we have a length-7 filter, which implies that the filter has 7 taps or coefficients. Each tap represents a specific weight or gain applied to a delayed version of the input signal. To achieve a minimum-multiplier realization, we can exploit the symmetry properties of the filter coefficients.
By carefully analyzing the symmetry properties, we can design a structure that reduces the number of required multipliers. For a length-7 Type 3 Linear Phase FIR Filter, the minimum-multiplier realization can be achieved by utilizing symmetric and anti-symmetric coefficients. The symmetric coefficients have the same value at equal distances from the center tap, while the anti-symmetric coefficients have opposite values at equal distances from the center tap.
By taking advantage of these symmetries, we can effectively reduce the number of multipliers needed to implement the filter. This results in a more efficient and resource-friendly design.
Learn more about multiplier
brainly.com/question/31406180
#SPJ11
True or False: Write T for True and F for False only. The delta configuration is commonly used in SOURCE side. True or False: Write T for True and F for False only. The wye configuration is commonly used in SOURCE side.
The delta connection is commonly used in DISTRIBUTION systems, not source side. The delta (Δ) configuration is also called as the mesh or closed delta. It is called mesh as it forms a closed loop which looks similar to a fishnet or mesh or net. This closed delta arrangement is usually used in transformer windings and motor windings. Hence, the given statement is false.
The wye (Y) configuration is also called a star or connected to ground. It is called connected to ground as it usually has the neutral point connected to ground. This wye arrangement is used in the transformer and generator windings. Hence, the given statement is true.
Learn more about delta configuration at
https://brainly.com/question/32659172
#SPJ11
2 Decane (C10H22) is burnt in a steady flow combustion chamber with 140% theoretical dry air. The flow rate of the fuel is 0.05 kg/min. (a) Derive the stoichiometric and actual combustion equations. (8 marks) (b) Determine the air-to-fuel ratio and required air flow rate. (4 marks) (c) Derive the wet volumetric analysis of the products of combustion. (8 marks) (d) In the case of the actual combustion process, calculate the average molecular weight in kg/kmol) of the exhaust mixture of gases. (5 marks)
The stoichiometric combustion equation for 2 Decane (C10H22) is given below.C10H22 + 15 (O2 + 3.76 N2) → 10 CO2 + 11 H2O + 56.4 N2The air required for the combustion of one kilogram of fuel is called the theoretical air required. F
or 2 Decane (C10H22), the theoretical air required can be calculated as below. Theoretical air = mass of air required for combustion of 2 Decane / mass of 2 Decane The mass of air required for combustion of 1 kg of 2 Decane can be calculated as below.
Molecular weight of C10H22 = 142 g/molMolecular weight of O2 = 32 g/molMolecular weight of N2 = 28 g/molMass of air required for combustion of 1 kg of 2 Decane = (15 × (32/142) + (3.76 × 15 × (28/142))) = 51.67 kg∴ The theoretical air required for 2 Decane (C10H22) combustion is 51.67 kg. The stoichiometric combustion equation is already derived above. Actual combustion equation:
To know more about combustion visit:-
https://brainly.com/question/32250637
#SPJ11
(a) Water is pumped through a rising main of a high rise building to a roof tank. The flow is predicted to be bubbly. Model the flow as pseudo two phase. (i) Give at least FOUR assumptions applied to your model. (2 Marks) Determine the power rating of a centrifugal pump with hydraulic efficiency 87% and electrical (motor) efficiency 75% for this flow system. The following data are provided; (Pipe dia = 65 mm, pipe length = 60 m. The upward flow is a mixture = 0.42 kg/s, P. = 103 kg/m?) and air bubbles (m, = 0.01 kg/s, P, = 1.1777 kg/m3). (8 Marks) of water, m
The power rating of the centrifugal pump for this flow system is 2.05 kW.
To model the flow as pseudo two-phase, we make the following assumptions:
1. Homogeneous Flow: The flow is assumed to be well mixed, with a uniform distribution of bubbles throughout the water. This allows us to treat the mixture as a single-phase fluid.
2. Negligible Bubble Coalescence and Breakup: We assume that the bubbles in the flow neither combine nor break apart significantly during the pumping process. This simplifies the analysis by considering a constant bubble size.
3. Negligible Slip between Phases: We assume that the water and air bubbles move together without significant relative motion. This assumption allows us to treat the mixture as a single fluid, eliminating the need for separate equations for each phase.
4. Steady-State Operation: We assume that the flow conditions remain constant over time, with no transient effects. This simplifies the analysis by considering only the average flow behavior.
To determine the power rating of the centrifugal pump, we can use the following equation:
Power = (Hydraulic Power)/(Overall Efficiency)
The hydraulic power can be calculated using:
Hydraulic Power = (Flow Rate) * (Head) * (Fluid Density) * (Gravity)
The flow rate is the sum of the water and air bubble mass flow rates, given as 0.42 kg/s and 0.01 kg/s, respectively. The head is the height difference between the pump and the roof tank, which can be calculated using the pipe length and assuming a horizontal pipe. The fluid density is the water density, given as 103 kg/m^3.
The overall efficiency is the product of the hydraulic efficiency and electrical efficiency, given as 87% and 75%, respectively.
Plugging in the values and performing the calculations, we find that the power rating of the centrifugal pump is 2.05 kW.
Learn more about pseudo two-phase
brainly.com/question/26335349
#SPJ11
Name the eight key elements recommended for an Ergonomics Program as presented in the OSHA Meatpacking Guidelines?
The OSHA Meatpacking Guidelines recommend the following eight key elements for an Ergonomics Program in the meatpacking industry:
These key elements are designed to help prevent and mitigate ergonomic hazards in the meatpacking industry, reducing the risk of work-related injuries and promoting a safer working environment for employees.
Management Commitment and Employee Involvement: Management should demonstrate a commitment to ergonomics by allocating resources, establishing policies, and involving employees in the decision-making processWorksite Analysis: Conduct a thorough analysis of the worksite to identify ergonomic risk factors, such as repetitive motions, awkward postures, and heavy lifting.
Hazard Prevention and Control: Implement measures to prevent and control ergonomic hazards, including engineering controls, administrative controls, and personal protective equipment (PPE). Training: Provide training to employees on ergonomics awareness, hazard recognition, and safe work practices to minimize the risk of musculoskeletal disorders (MSDs).
Medical Management: Develop protocols for early detection and management of work-related MSDs, including prompt reporting, medical evaluation, treatment, and rehabilitation.
Program Evaluation: Regularly assess the effectiveness of the ergonomics program, identify areas for improvement, and make necessary adjustments.Recordkeeping and Program Documentation: Maintain records related to ergonomics program activities, including assessments, training, incident reports, and corrective actions.
Management Review: Conduct periodic reviews of the ergonomics program to ensure its continued effectiveness and make any necessary updates or revisions.
These key elements are designed to help prevent and mitigate ergonomic hazards in the meatpacking industry, reducing the risk of work-related injuries and promoting a safer working environment for employees.
Learn more about Ergonomics here
https://brainly.com/question/28706393
#SPJ11
Which one of the following statements on Darcy-Weisbach's formula is correct? O Darcy-Weisbach's formula is generally used for head loss in flow through both pipes and Chezy's formula for open channels O Chezy's formula is generally used for head loss in flow through both pipes and Darcy-Weisbach's formula for open channels Chezy's formula is generally used for head loss in flow through both pipes and open channels Darcy-Weisbach's formula is generally used for head loss in flow through both pipes and open channels
The correct statement is: Darcy-Weisbach's formula is generally used for head loss in flow through both pipes and open channels.
The Darcy-Weisbach equation is a widely accepted formula for calculating the head loss due to friction in pipes and open channels. It relates the head loss (\(h_L\)) to the flow rate (\(Q\)), pipe or channel characteristics, and the friction factor (\(f\)).
The Darcy-Weisbach equation for head loss is:
[tex]\[ h_L = f \cdot \frac{L}{D} \cdot \frac{{V^2}}{2g} \][/tex]
Where:
- \( h_L \) is the head loss,
- \( f \) is the friction factor,
- \( L \) is the length of the pipe or channel,
- \( D \) is the diameter (for pipes) or hydraulic radius (for open channels),
- \( V \) is the velocity of the fluid, and
- \( g \) is the acceleration due to gravity.
Chezy's formula, on the other hand, is an empirical formula used to calculate the mean velocity of flow in open channels. It relates the mean velocity (\( V \)) to the hydraulic radius (\( R \)) and a roughness coefficient (\( C \)).
Learn more about Darcy-Weisbach's formula here:
https://brainly.com/question/30853813
#SPJ11
A semiconductor material has a spontaneous emission rate Rsp R₁ under thermal equilibrium. (i) Assuming n。 = P₁, calculate the exact value of the required concentration of excess carriers, An, such that the new total spontaneous emission rate under excitation, R₂, is equal to 10¹ (R₁). Write the answer in terms of no. (10 points) (ii) Show that doubling An from Part (i) results in a new spontaneous emission rate, R3, that is approximately equal to 4R₂. (10 points)
The spontaneous emission rate refers to the rate at which photons are emitted by excited atoms or electrons in a material without any external stimulation. It is a fundamental process in which an excited state transitions to a lower energy state by emitting a photon. The spontaneous emission rate depends on various factors such as the energy level structure of the material, temperature, and other physical properties. It is typically represented by the symbol Rsp. doubling An from Part (i) results in a new spontaneous emission rate (R3) that is approximately equal to 4 times R₂.
(i) To calculate the required concentration of excess carriers (An) such that the new total spontaneous emission rate under excitation (R₂) is equal to 10¹ times the initial spontaneous emission rate (R₁), we can set up the equation:
R₂ = R₁ + An
Since we want R₂ to be 10 times R₁, we have:
10R₁ = R₁ + An
Simplifying the equation, we find:
An = 9R₁
Therefore, the required concentration of excess carriers (An) is equal to 9 times the initial spontaneous emission rate (R₁).
(ii) Doubling An from Part (i) means that the new concentration of excess carriers ([tex]A_2n[/tex]) is 2An. We need to find the new spontaneous emission rate ([tex]R_3[/tex]) in terms of R₂.
[tex]R_3[/tex] = R₂ + A2n
Substituting the value of A2n, we get:
([tex]R_3[/tex]) = R₂ + 2An
Since An is 9R₁ (as found in Part i), we have:
([tex]R_3[/tex]) = R₂ + 2(9R₁)
([tex]R_3[/tex])= R₂ + 18R₁
Approximately, ([tex]R_3[/tex]) is equal to 4 times R₂ (4R₂).
Therefore, doubling An from Part (i) results in a new spontaneous emission rate (R3) that is approximately equal to 4 times R₂.
Learn more about spontaneous emission rate here:
brainly.com/question/33223630
#SPJ11
Environmental impact of pump hydro station.
question:
1. What gains are there from using this form of the hydro pump station compared to more traditional forms (if applicable)
2. What are the interpendencies of this pump hydro station with the environment?.
3. We tend to focus on negative impacts, but also report on positive impacts.
The pump hydro station has both positive and negative impacts on the environment.
The Pump Hydro Station is one of the widely used hydroelectricity power generators. Pump hydro stations store energy and generate electricity when there is an increased demand for power. Although this method of producing electricity is efficient, it has both negative and positive impacts on the environment.Negative Impacts: Pump hydro stations could lead to the loss of habitat, biodiversity, and ecosystems. The building of dams and reservoirs result in the displacement of people, wildlife, and aquatic life. Also, there is a risk of floods, landslides, and earthquakes that could have adverse impacts on the environment. The process of generating hydroelectricity could also lead to the release of greenhouse gases and methane.
Positive Impacts: Pump hydro stations generate renewable energy that is sustainable, efficient, and produces minimal greenhouse gases. It also supports the reduction of greenhouse gas emissions. Pump hydro stations provide hydroelectricity that is reliable, cost-effective, and efficient in the long run. In conclusion, the pump hydro station has both positive and negative impacts on the environment. Therefore, it is necessary to evaluate and mitigate the negative impacts while promoting the positive ones. The hydroelectricity generation industry should be conducted in an environmentally friendly and sustainable manner.
Know more about hydro station, here:
https://brainly.com/question/32136412
#SPJ11
Score =. (Each question Score 12points, Total Score 12 points ) An information source consists of A, B, C, D and E, each symbol appear independently, and its occurrence probability is 1/4, 1/8, 1/8, 3/16 and 5/16 respectively. If 1200 symbols are transmitted per second, try to find: (1) The average information content of the information source; (2) The average information content within 1.5 hour. (3) The possible maximum information content within 1 hour.
Sure, I can help you with that.
1. The average information content of the information source
The average information content of an information source is calculated by multiplying the probability of each symbol by its self-information. The self-information of a symbol is the amount of information that is conveyed by the symbol. It is calculated using the following equation:
```
H(x) = -log(p(x))
```
where:
* H(x) is the self-information of symbol x
* p(x) is the probability of symbol x
Substituting the given values, we get the following self-information values:
* A: -log(1/4) = 2 bits
* B: -log(1/8) = 3 bits
* C: -log(1/8) = 3 bits
* D: -log(3/16) = 2.5 bits
* E: -log(5/16) = 2.3 bits
The average information content of the information source is then calculated as follows:
```
H = p(A)H(A) + p(B)H(B) + p(C)H(C) + p(D)H(D) + p(E)H(E)
```
```
= (1/4)2 + (1/8)3 + (1/8)3 + (3/16)2.5 + (5/16)2.3
```
```
= 1.8 bits
```
Therefore, the average information content of the information source is 1.8 bits.
2. The average information content within 1.5 hour
The average information content within 1.5 hour is calculated by multiplying the average information content by the number of symbols transmitted per second and the number of seconds in 1.5 hour. The number of seconds in 1.5 hour is 5400.
```
I = H * 1200 * 5400
```
```
= 1.8 bits * 1200 * 5400
```
```
= 11664000 bits
```
Therefore, the average information content within 1.5 hour is 11664000 bits.
3. The possible maximum information content within 1 hour
The possible maximum information content within 1 hour is calculated by multiplying the maximum number of symbols that can be transmitted per second by the number of seconds in 1 hour. The maximum number of symbols that can be transmitted per second is 1200.
```
I = 1200 * 3600
```
```
= 4320000 bits
```
Therefore, the possible maximum information content within 1 hour is 4320000 bits.
Learn more about information theory here:
https://brainly.com/question/31566776
#SPJ11