Let us take the initial distance between car A and B as d₀. Let the time taken by car A to stop after it starts decelerating at a be t seconds. Now, the acceleration of car A = a (given), which is constant and negative (because it is decelerating).
Therefore, the velocity of car A after t seconds, vA
= uA + at
= va – at …(1) (where uA
= va is the initial velocity)The distance traveled by car A after t seconds, dA
The velocity of car B, vb, remains constant at vb throughout. So, the distance traveled by car B during this time t,
dB = vb × t …(3)
Now, we can use the equation of motion: for calculating the distance traveled by car A and B, respectively, where s = d₀ (initial distance between the cars) – d (distance between the cars at time t).Applying the equation to car A,
dA = (va + vA)t/2
= (va + va - at)t/2
= (2va - at)t/2
= va × t - (1/2)at² …(4) (using equation (1))
Applying the same equation to car B,
dB = (vb + vb)t/2
= vb × t …(5) (using equation (3))
We know that when car A stops, its velocity vA = 0.So, from equation (1), we get t = va/a. Substituting this value of t in equation (4) and (5), we get:dA = va²/2a …(6)and dB = vb × va/a …(7). Subtracting equation (7) from (6), we get the distance d between the cars at the instant car A stops.
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29 10 1 point According to Gate Theory, which of the following factors can make you more sensitive to pain? Placebo effects Competing signals, like rubbing your elbow Chronic stress High levels of arousal 30 1 point Patients who are allowed to self-administer morphine use less than when they receive injections from healthcare providers. True False 31 1 point What happens when people lose their sense of smell (olfaction)? They often become manic. 32 Not much. Olfaction is not a very important sense for humans. They compensate by developing an increased sensitivity to taste (gustation). They often become depressed. 1 point The different taste qualities (sweet, sour, bitter, salt, umami) each have their own area of the tongue that is most sensitive to them. True False
The statement that The different taste qualities (sweet, sour, bitter, salt, umami) each have their own area of the tongue that is most sensitive to them is False.
Gate Theory states that competing signals such as rubbing your elbow can make you more sensitive to pain. This theory suggests that physical signals such as massage, pressure, heat, or cold can block the transmission of pain messages through the spinal cord and prevent them from reaching the brain. Therefore, when people rub their elbows or apply pressure to the area, this stimulates the non-painful touch fibers and decreases the transmission of the painful stimuli.
As per the statement, patients who are allowed to self-administer morphine use less than when they receive injections from healthcare providers is True. Olfaction is a very important sense for humans, and they often become depressed when they lose their sense of smell (olfaction). The statement that The different taste qualities (sweet, sour, bitter, salt, umami) each have their own area of the tongue that is most sensitive to them is False.
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. given only 2-input nand, nor, xor, xnor gates, and inverters, which is the preferred set of control signals?
A set of control signals is a group of inputs to a digital circuit that determine its response. These control signals govern the operation of the circuit and determine its logical functionality.
The ideal set of control signals that are used in a digital circuit depends on the requirement of the circuit. As given, we have only 2-input NAND, NOR, XOR, XNOR gates, and inverters, which means we cannot make all other gates, and we have to select the appropriate set of control signals.Among the given gates, NAND and NOR gates can be used to implement all other logic gates. XOR gate can be obtained by combining NAND gates and inverters, while XNOR gate can be obtained by using NOR gates and inverters. However, when we use only NAND and NOR gates, the size of the circuit increases. Therefore, the preferred set of control signals among the given gates should be the combination of XOR and inverters.The XOR gate requires less logic than the implementation of XOR using NAND and NOR gates. The XOR gate can be used as a universal gate and is also used in various arithmetic and encryption circuits. Therefore, the preferred set of control signals should be XOR and inverters.
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when the same presynaptic neuron fires at 20 aps per second, however, the postsynaptic cell fires. this is an example of
When the same presynaptic neuron fires at 20 aps per second, however, the postsynaptic cell fires; this is an example of a convergent neural pathway.What is a neural pathway?A neural pathway refers to the network of nerve fibers or neurons that conduct nerve impulses from one part of the body to another.
The transmission of information from one neuron to another is mediated by the release of chemical neurotransmitters, which bind to receptors on the postsynaptic membrane of the next neuron in line. This process results in the transmission of information from one neuron to the next.
Consequently, when the same presynaptic neuron fires at 20 aps per second, however, the postsynaptic cell fires, this is an example of a convergent neural pathway in action. In other words, the postsynaptic neuron is receiving input from multiple sources and is responding based on the relative strengths of those signals.
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Jess likes to play Mario Bros on the Nintendo Entertainment System (NES). In what
era were these gaming systems first released?
(1 point)
1970s
1980s
1990s
O2000s
The very first Nintendo Entertainment System (NES) came out in October 18, 1985. So, it would be in the 1980s.
-------------------------------------------
Hope this helps!
Have a great day and God bless! :)
When a ship arrives at a harbor, it is docking at one of six berths. If all six berths are occupied, the ship leaves the harbor immediately. After docking at a berth, the ship waits for the unloading service of a single crane. The crane unloads the ships in a First-In-First-Out discipline. After unloading, the ship leaves the harbor immediately. Define the system state at time t as [U(t),C(t)], where U(t)= number of ships waiting to be unloaded or being unloaded C(t)= number of busy cranes ( 0 or 1 ) Let [u,c] be the current state of the system. Define events and write the corresponding state transitions
The given problem describes a docking system of ships at a harbor. When a ship arrives at the harbor, it docks at one of six berths. If all six berths are occupied, the ship leaves the harbor immediately. After docking, the ship waits for the unloading service of a single crane. The crane unloads the ships in a First-In-First-Out discipline.
After unloading, the ship leaves the harbor immediately. The system state at time t is defined as [U(t),C(t)] where U(t) represents the number of ships waiting to be unloaded or being unloaded and C(t) represents the number of busy cranes (0 or 1). Let [u, c] be the current state of the system.
Now, the state transitions can be defined as follows:
Events:
1. A ship arrives at the harbor and all berths are occupied
2. A ship arrives at the harbor and some berths are empty
3. A crane becomes available
4. A ship finishes unloading and leaves the harbor
State transitions:
1. If [u, c] = [6, 1], the ship leaves the harbor immediately. The system state remains [6, 1].
2. If [u, c] = [6, 0], the ship leaves the harbor immediately. The system state remains [6, 0].
3. If [u, c] = [0, 0], the system state becomes [0, 1].
4. If [u, c] = [n, 0] (where n is less than 6), the system state becomes [n+1, 0].
5. If [u, c] = [n, 1] (where n is less than 6), the system state becomes [n, 1].
6. If [u, c] = [1, 1], the system state becomes [0, 1].
7. If [u, c] = [n, 1] (where n is greater than 1), the system state becomes [n-1, 1].
8. If [u, c] = [0, 1], the system state remains [0, 1].
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A forklift will tip over if the center of gravity is outside the stability triangle. True or false?
Answer:
True
Explanation:
A forklift will tip over if the center of gravity is outside the stability triangle. The stability triangle refers to the area within the three wheels of a forklift that ensures the stability of the machine and prevents tipping. If the center of gravity of the load being carried by the forklift moves outside of the stability triangle, the machine becomes unstable and is at risk of tipping over. It's important to properly balance the load on a forklift and ensure that the center of gravity stays within the stability triangle to avoid accidents and maintain safety.
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What is the formula for resultant force
Answer:
F = 3 N + 2 N = 5 N
Explanation:
Resultant force F = 3 N + 2 N = 5 N to the right. The resultant force is 5 N to the right. Two forces that act in opposite directions produce a resultant force that is smaller than either individual force. To find the resultant force subtract the magnitude of the smaller force from the magnitude of the larger force.
Generally, the primary source of all water supply is said to be
Find the voltage gain v0/vs of the circuit given below, where R1 = 14 kΩ and R2 = 13 kΩ
Answer:
The voltage gain is 2.07.
Explanation:
Given that,
Resistance \(R_{1}=14\ k\Omega\)
Resistance \(R_{2}=13\ k\Omega\)
We need to calculate the voltage gain
Using formula of voltage source
\(V_{s}=\dfrac{V_{o}\times R_{2}}{R_{1}+R_{2}}\)
\(\dfrac{V_{o}}{V_{s}}=\dfrac{R_{1}+R_{2}}{R_{2}}\)
Where, \(R_{1}\) = first resistance
\(R_{2}\) =second resistance
\(V_{s}\) = source voltage
\(V_{o}\) = output voltage
Put the value into the formula
\(\dfrac{V_{o}}{V_{s}}=\dfrac{14+13}{13}\)
\(\dfrac{V_{o}}{V_{s}}=2.07\)
Hence, The voltage gain is 2.07
_____________ processes are actions that create physical solutions to problems.
a
Production Processes
b
Medical Processes
c
Agricultural Processes
d
Communication Process
Answer:
yes answer d is correct
Communication Process are actions that create physical solutions to problems. The correct option is d.
What is Communication Process?Human existence and organisational survival both depend on effective communication. It is a process of generating and disseminating thoughts, facts, opinions, and sentiments from one place, individual, or group to another. The Management function of Directing depends on effective communication.
The sending party, message encoding, channel selection, message receipt by the recipient, and message decoding are all aspects of the communication process.
Feedback is when the recipient communicates something back to the original sender. These procedures are actions that result in tangible fixes for issues.
Thus, the correct option is d.
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Taking the convection heat transfer coefficient on both sides of the plate to be 860 W/m2 ·K, deter- mine the temperature of the sheet metal when it leaves the oil bath. Also, determine the required rate of heat removal from the oil to keep its temperature constant at 45°C.
Answer:
Hello your question is incomplete attached below is the complete question
answer :
a) 95.80°C
b) 8.23 MW
Explanation:
Convection heat transfer coefficient = 860 W/m^2 . k
a) Calculate for the temp of sheet metal when it leaves the oil bath
first step : find the Biot number
Bi = hLc / K ------- ( 1 )
where : h = 860 W/m^2 , Lc = 0.0025 m , K = 60.5 W/m°C
Input values into equation 1 above
Bi = 0.036 which is < 1 ( hence lumped parameter analysis can be applied )
next : find the time constant
t ( time constant ) = h / P*Cp *Lc --------- ( 2 )
where : p = 7854 kg/m^3 , Lc = 0.0025 m , h = 860 W/m^2, Cp = 434 J/kg°C
Input values into equation 2 above
t ( time constant ) = 0.10092 s^-1
Determine the elapsed time
T = L / V = 9/20 = 0.45 min
∴ temp of sheet metal when it leaves the oil bath
= (T(t) - 45 ) / (820 - 45) = e^-(0.10092 * 27 )
T∞ = 45°C
Ti = 820°C
hence : T(t) = 95.80°C
b) Calculate the required rate of heat removal form the oil
Q = mCp ( Ti - T(t) ) ------------ ( 3 )
m = ( 7854 *2 * 0.005 * 20 ) = 26.173 kg/s
Cp = 434 J/kg°C
Ti = 820°C
T(t) = 95.80°C
Input values into equation 3 above
Q = 8.23 MW
the concrete slab for the trash enclosure is ____
The concrete slab for the trash enclosure is properly designed, reinforced, and cured. It ensures adequate strength and durability for supporting the weight of the trash bins and resisting weather elements.
Firstly, the concrete mix must be selected to meet the requirements of the specific trash enclosure, taking into account factors like strength, durability, and resistance to weather elements. The mix typically includes cement, sand, aggregate, and water, with proportions adjusted according to the desired properties.
Next, the slab's reinforcement is crucial to maintain structural integrity and prevent cracking under load. Reinforcing steel bars, or rebar, are placed within the slab's formwork before pouring the concrete mix. The rebar spacing and size should follow applicable building codes and design specifications.
After preparing the formwork and reinforcing bars, the concrete mix is poured into the form, filling it completely. During the pouring process, it's essential to ensure even distribution of the mix and avoid air pockets or voids, which can lead to weak spots in the slab. This can be achieved by using a vibrating tool to consolidate the mix and remove trapped air.
Once the concrete is poured, it must be screeded to create a level and smooth surface. After screeding, the concrete needs to be finished and cured properly to achieve its full strength and durability. The curing process typically involves maintaining the slab's moisture and temperature within specific limits for a minimum period, usually around 28 days.
In summary, the concrete slab for the trash enclosure must be well-designed, reinforced, and cured to provide a robust and durable foundation for the enclosure's function and longevity.
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Exercise 2. [30 points). Give a deterministic finite automaton for the language L of non-empty (length greater than zero) binary strings which contain no pair of consecutive 1s. For example, the strings 00000, 1, 1000101001, and 00010 are all in L, but 00110 is not.
By following these transitions, the DFA can determine if a given binary string is in the language L, which consists of non-empty strings without consecutive 1s.
Explain the concept of polymorphism in object-oriented programming?The DFA has three states: q0, q1, and q2.The start state is q0, which represents the initial state of reading a binary string.The accept states are q0 and q1, which represent the states where a valid string without consecutive 1s ends.The transitions define the behavior of the DFA based on the input.If the current state is q0 and the input is 0, it remains in q0, representing that the string can continue without violating the condition.If the current state is q0 and the input is 1, it goes to q1, indicating that a single 1 is valid, and the next character should not be 1.If the current state is q1 and the input is 0, it goes to q2, indicating that a 0 after a valid 1 is allowed, but consecutive 1s should not occur.If the current state is q1 and the input is 1, it stays in q1, representing that consecutive 1s are not allowed, and the string is invalid.If the current state is q2, it remains in q2 regardless of the input, as consecutive 1s have already been encountered and the string is invalid.Learn more about non-empty strings
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quizzlet in general, the minimum-size aluminum feeder conductors permitted to be installed in parallel is ?
The minimum size of aluminum feeder conductors permitted to be installed in parallel is #1/0 AWG.
What is an Aluminum Feeder conductor?A feeder conductor is an electrical power cable that carries electricity from a distribution point to the point of use. The current-carrying conductors that come from the distribution point or transformer and feed directly into the facility are known as feeder conductors. Aluminum is a popular choice for wiring as well as electrical conductor applications in the power industry.
The reason for this is because it has some desirable characteristics such as low resistance, low cost, and low weight. Here are the aluminum conductor sizes:#1/0 AWG (minimum size)1/0 AWG2/0 AWG3/0 AWG4/0 AWG. The above-listed wire sizes are commonly used as feeders or sub-feeders, and the smallest allowable wire size for parallel conductors is 1/0 AWG.
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Identify the best drying agent or process for each described purpose. Removal of small amounts of water from a polar solvent____. Removal of visible pockets of water from an organic solvent____. Storage of solvents or other materials in a desiccator_____.
Answer:
Calcium Chloride
Brine Wash
Drierite
Explanation:
Removal of small amounts of water from a polar solvent is Calcium Chloride
Removal of visible pockets of water from an organic solvent is Brine Wash
Storage of solvents or other materials in a desiccator is Drierite
what is the dimensions of beta
Answer:
byee byee bbbbbbbbbbbb
Simplify the expression below:
313 + 12 =
ANSWER :
325
Explanation:
313 + 12 = 325
When you grip a vehicle’s steering wheel with both hands, a couple moment is applied to the wheel.
Would older vehicles without power steering have larger or smaller steering wheels? What could be the reason having (larger or smaller) steering wheels?
Larger steering wheels were typically found on older, non-power steering automobiles. Larger steering wheels have a mechanical advantage over smaller ones, enabling drivers to turn with more force.
Why are steering wheels on new, contemporary cars smaller than those on older cars?A lower diameter allows for a more comfortable driving position as well as more space between the seat and the steering wheel.
Why does the steering on older automobiles seem loose?Over time, tie rods frequently sustain significant wear and tear. The tie rods are put to frequent use each time you turn your wheel, but they also serve as a major vibration absorber for the wheels.
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Does a bridge anchored resting on two pillars have any torque?.
Answer: Yes, but it is at equilibrium
Explanation:
This graph shows the US unemployment rate from
August 2010 to November 2011
The graph could help an economist predict that how many people will be out of work in the next year. The correct option is c.
What is unemployment?
Unemployment is the condition where people who have knowledge or eligible for doing job, but they are not getting job. Unemployment is the scarcity of jobs.
The options are attached:
a. how the government will address unemployment.
b. why workers might have a harder time finding jobs.
c. how many people will be out of work in the next year.
d. why producers might hire fewer workers in the future.
Thus, the correct option is c. how many people will be out of work in the next year.
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Answer:
b. will continue to rise.
Complete Question:
This graph shows the US unemployment rate from August 2010 to November 2011.
This graph suggests unemployment in the United States
a. will continue to fall.
b. will continue to rise.
c. will remain the same.
d. will only change a little.
b. will continue to rise.
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4. It is always the employee's responsibility to make sure they wear their respirator.
A) True
B)
False
Answer:
the answer for this question is true
Question:
It is always the employee's responsibility to make sure they wear their respirator. A) True B) False
Answer:
The answer to this question would be A. True
Explanation:
It would be the employee's responsibility the boss/manager should not have to tell them to put it on. If you don't know what a respirator is it's worn over the mouth and nose as a mask to prevent the inhalation of dust, and other chemicals and stuff.
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What is the maximum number of points a player can score during a frame of snooker while curving around at a 45 degree angle going at a speed of 2 miles per hour with the wind speed of 2 mph on a rug coated snooker table?
In snooker, the maximum number of points that can be scored during a single frame is 147. This is achieved by potting all 15 red balls, each worth 1 point, and subsequently potting the colored balls in sequence: yellow (2 points), green (3 points), brown (4 points), blue (5 points), pink (6 points), and black (7 points). Each color is then returned to its original position and can be potted again for additional points.
The angle and wind speed mentioned in your question are not relevant to determining the maximum number of points in a snooker frame. The speed and direction of the balls are controlled by the player's shots, and the rug coating on the table doesn't affect the scoring.
So, regardless of the angle, wind speed, or table surface, the maximum number of points that can be scored in a frame of snooker is 147.
Question 1
a) In Matlab, read the following sentence and record your own voice for 4 seconds at a rate
40 kHz and generate a “message.wav” file.
“Use a pencil to write the first draft.”
b) Downsample your message signal at a sampling rate 8 kHz, show the original signal and
its discrete time samples for a very short period of time.
c) Using Spectrum Analyzer, show the two sided spectrum of the original signal and the
sampled signal.
d) Define a low pass filter with suitable cutoff frequencies to recover the original low pass
filter from its discrete time samples. Listen the original message signal and recovered
message signal at 40 kHz and comment on your results.
e) Repeat the above steps for the new sampling rate 4 kHz. What happens at 4 kHz?
Comment on your results.
Question 2
a) In Matlab, read the following sentences and record your own voice for 4 seconds at a
rate 40 kHz and generate “message1.wav” and “message2.wav” files.
“The two met while playing on the sand.”
“This is a grand season for hikes on the road.”
b) In Matlab, implement an analog QAM modulator with carrier frequency 8 kHz. Show the
two sided QAM spectrum using Spectrum Analyzer.
c) Add Gaussian channel noise whose power is 1 micro Watts.
d) Implement QAM demodulator and recover message 1 and message 2. Listen the original
message signals and recovered message signals and comment on your results.
e) Repeat the above steps with channel noise whose power is 1 milliWatts. Comment on
your results.
Question 3
In this question, you are NOT allowed to use “ssbmod” and “ssbdemod” functions.
a) In Matlab, read the following sentence and record your own voice for 4 seconds at a rate
40 kHz and generate “message.wav” file,
“We find joy in the simplest things. “
b) In Matlab, implement an USB modulator with carrier frequency 8 kHz. Show the two
sided USB spectrum and DSB spectrum using Spectrum Analyzer.
c) Add Gaussian channel noise whose power is 1 micro Watts.
d) Implement USB/LSB demodulators and recover the message. Listen the original message
signals and recovered message signals and comment on your results.
e) Repeat the above steps with channel noise whose power is 1 milliWatts. Comment on
your results.
a) To record a voice message in Matlab, you can use the "audiorecorder" function. The code for recording the message for 4 seconds at a rate of 40 kHz and saving it as a "message.wav" file would be:
recObj = audiorecorder(40000, 16, 1);
disp('Start speaking.')
recordblocking(recObj, 4);
disp('End of Recording.');
message = getaudiodata(recObj);
audiowrite('message.wav', message, 40000);
b) To downsample the message signal at a sampling rate of 8 kHz, we can use the "resample" function. The code for showing the original signal and its discrete time samples for a short period of time would be:
t = 0:1/40000:0.001;
t_ds = 0:1/8000:0.001;
message_ds = resample(message, 1, 5);
plot(t, message, 'b', t_ds, message_ds(1:length(t_ds)), 'r*');
xlabel('Time (s)');
ylabel('Amplitude');
legend('Original signal', 'Discrete time samples');
c) To show the two-sided spectrum of the original and sampled signal, we can use the "fft" function. The code would be:
N = length(message);
N_ds = length(message_ds);
f = (-N/2:N/2-1)(40000/N);
f_ds = (-N_ds/2:N_ds/2-1)(8000/N_ds);
spectrum = abs(fftshift(fft(message)));
spectrum_ds = abs(fftshift(fft(message_ds)));
plot(f, spectrum, 'b', f_ds, spectrum_ds, 'r');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
legend('Original signal', 'Sampled signal');
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Which option distinguishes the type of software the team should use in the following scenario?
A development team needs to create a code of detailed instructions for producing automobile dashboards for a large United States automaker.
a. computer-aided engineering software
b. digital manufacturing software
c. geographic mapping software
d. computer-aided manufacturing software
Which type of engineer finds his or her skills needed in the electronics, architectural, medical, and aerospace industries?
nuclear engineer
chemical engineer
biomedical engineer
mechanical engineer
Answer:
mechanical engineer
Explanation:
8. Find the volume of the figure shown below: * V=L x W x H 7 cm 2 cm 2 cm
Consider a 3-km2 urban catchment. The main channel has a slope of 0.9% and a Manning n of 0.10. The catchment is 50% impervious. The distance along the main channel from the catchment boundary to the outlet is 1100 m. The urban catchment has an average curve number of 60. Determine the peak flow (m3 /s) of the NRCS unit hydrograph for a 20-min rainfall excess.
Answer:
The right answer is "5.105×10⁸ m³/sec".
Explanation:
The given values are:
Catchment area,
A = 3 km²
Length to watershed,
L = 1100 m
Average watershed slope,
S = 0.9% i.e., 0.009
Curve number,
CN = 60
Rainfall duration,
D = 20 min
Let,
Time form beginning of the rainfall will be "\(t_p\)".Lag time will be "\(t_1\)".Now,
⇒ \(t_1=\frac{L^{0.8}\times (\frac{1000}{CN} -9)^{0.7}}{19000S^{0.5}}\)
On substituting the values, we get
⇒ \(t_1=\frac{1100^{0.8}\times (\frac{1000}{60} -9)^{0.7}}{19000\times 0.009^{0.5}}\)
⇒ \(=0.625 \ hours\)
then,
⇒ \(T_p=\frac{D}{2}+t_1\)
⇒ \(=\frac{0.33}{2}+0.625\)
⇒ \(=\frac{0.33+1.25}{2}\)
⇒ \(=\frac{1.58}{2}\)
⇒ \(=0.79 \ hr\)
hence,
The peak flow will be:
⇒ \(Q_p=\frac{484A}{t_p}\)
⇒ \(=\frac{484\times 3}{0.79}\)
⇒ \(=\frac{1452}{0.79}\)
⇒ \(=1837.97 \ km^3/hr\)
or,
⇒ \(=5.105\times 10^8 \ m^3/sec\)
A piston–cylinder device contains 15 kg of saturated refrigerant-134a vapor at 280kPa. A resistance heater inside the cylinder with a value of 110V is used to transfer heat of 20.67kJ/kg to the refrigerant at constant pressure for 6min. Determine the current supplied if the final temperature is 75℃
Answer:
18.77 A
Explanation:
To solve this we use the energy balance equation, that is:
\(E_{in}-E_{out}=\Delta E_{sys}\\\\Q_{in}+W_{in}+W_{out}=\Delta U\\\\Q_{in}+W_{in}=\Delta U\\\\But\ W_{in}=Voltage(V)*Current(I)*change\ in\ time(\Delta t)=VI\Delta t,\Delta U=m(h_2-h_1)\\\\Given\ that\ m=15kg,V=110\ V,\Delta t=6\ min = (6*60\ s)=360\ s,Q_{in}=20.67\ kJ/kg*15\ kg=310.05\ kJ=310050\ J\\\\From\ table: At\ P_1=280kPa, h_1=249.71\ kJ/kg=249710\ J/kg;At\ P_2=280kPa \ and\ T_1=75^oC,P_2=319.95\ kJ/kg=319950\ J/kg\\\\Substituting:\\\\310500+(110*360*I)=15(319950-249710)\\\\\)
\(39600I=1053600-310500\\\\39600I=743100\\\\I=18.77\ A\)
A rain gutter is to be constructed from a metal sheet of width 3m by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?.
The area of the gutter is therefore equal to the area of the rectangle plus the area of the triangles.
A = rectangle + 2 * triangle
= 10h + 2 * (1/2 hw)
Using trig work out h and w.
h = 10 sin ?
w = 10 cos ?
A = 10h + hw
= 100sin? + 100sin?cos?
Differentiate the expression (either use the product rule for sin? cos?, or write 100sin?cos? as 50sin2? using the double angle formula)
A = 100sin? + 50sin2?
dA/dt = 100cos? + 100cos2?
For A to be a max or min the derivative must equal zero
100cos? + 100cos2? = 0
cos? + cos2? = 0
Use the double angle formula to write cos2? as 2cos^2 ? - 1
cos? + 2cos^2 ? - 1 = 0
2cos^2 ? + cos? - 1 = 0
This quadratic factorizes:
(2cos? - 1)(cos? + 1) = 0
This means that
cos ? = 1/2 or cos ? = 1
giving:
? = pi/3 or ? = pi
Which means that to achieve the maximum area ? should be pi/3 = 60 degrees
You can check that this is the max by substituting in these values of theta and the two end points (theta = 0, theta = pi), and seeing that pi/3 gives the maximum.
The maximum area is therefore
A = 100sin? + 100sin?cos?
= 100sin(pi/3) + 100sin(pi/3)cos(pi/3)
= 100 sqrt(3) / 2 + 100 sqrt(3)/2 * 1/2
= 100 * 3/2 * sqrt(3) / 2
= 3 * 25 * sqrt(3)
= 75 sqrt(3)
= 129.9...
= 130 cm^3
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applying ‘engineering discipline’ to software engineering implies problem solving by a repeatable process that involves what four activities?
Applying ‘engineering discipline’ to software engineering implies problem solving by a repeatable process that involves four activities are design, developing, requirements, verification and testing.
When it comes to software engineering, the "engineering discipline" indicates problem solving through a cyclical process that includes the following four tasks:
Definition and documentation of the software system's functional and non-functional requirements, including user requirements, limitations, and specifications
Design: The process of producing a comprehensive blueprint or plan for the software system, including an interface design and database design.
Developing, testing, and debugging the software code to make sure it adheres to the requirements and design specifications constitute implementation.
Verification and testing: Assessing the software system to make sure it satisfies the requirements, operates as anticipated, and is durable and upgradable.
Software engineers employ these four processes, often referred to as the software development life cycle (SDLC), to build
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