The model is used to predict the XOR outputs for the given input values, and the predictions are printed.
To implement XOR with 2 hidden neurons and 1 output neuron, we can use a simple feedforward neural network with backpropagation. Here's an example program in Python using the Keras library:
```python
import numpy as np
from keras.models import Sequential
from keras.layers import Dense
# Define the XOR input and output
x = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])
# Create the neural network model
model = Sequential()
model.add(Dense(2, input_dim=2, activation='sigmoid')) # Hidden layer with 2 neurons
model.add(Dense(1, activation='sigmoid')) # Output layer with 1 neuron
# Compile the model
model.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])
# Train the model
model.fit(x, y, epochs=1000, verbose=0)
# Evaluate the model
loss, accuracy = model.evaluate(x, y)
print(f"Loss: {loss}, Accuracy: {accuracy * 100}%")
# Predict the XOR outputs
predictions = model.predict(x)
rounded_predictions = np.round(predictions)
print("Predictions:")
for i in range(len(x)):
print(f"Input: {x[i]}, Predicted Output: {rounded_predictions[i]}")
```
This program uses the Keras library to create a Sequential model, which represents a linear stack of layers. The model consists of one hidden layer with 2 neurons and one output layer with 1 neuron. The activation function used for both layers is the sigmoid function.
The model is trained using the XOR input and output data. The loss function used is mean squared error, and the optimizer used is Adam. The model is trained for 1000 epochs.
After training, the model is evaluated to calculate the loss and accuracy. The accuracy represents the percentage of correct predictions.
Finally, the model is used to predict the XOR outputs for the given input values, and the predictions are printed.
Note: The accuracy achieved by this simple model may vary, and it may not always reach a minimum of 3%. Achieving a higher accuracy for XOR using only 2 hidden neurons can be challenging. Increasing the number of hidden neurons or adding more layers can improve the accuracy.
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In terms of cars technology, does luxury equal safety, yes or no and why?
Since they are built to prevent collisions and offer more sophisticated safety and driver assistance features, luxury cars have a reputation for being among the safest automobiles on the road.
Are all automobiles similarly safe?Vehicles of all sizes are now safer because to advances in crash safety, yet even with these advancements, larger vehicles continue to be safer than smaller ones. Deaths in crashes decrease as vehicle size grows, as shown in the chart below.
What distinguishes expensive automobiles from everyday vehicles?Engines, transmissions, sound systems, telematics, safety features, and other equipment that aren't included in lower-priced models are frequently found in luxury cars, along with a plethora of other luxuries.
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if the low-pressure gauge reading creeps up after the torch valve is closed, you should immediately turn off the ____.
If the low-pressure gauge reading creeps up after the torch valve is closed, you should immediately turn off the gas cylinder valve.
When the low-pressure gauge reading continues to increase after the torch valve is closed, it indicates a potential issue with the gas supply system. This can be a sign of a faulty regulator, a leak in the system, or an obstruction. In such a situation, it is crucial to take immediate action to prevent any safety hazards or damage.
By turning off the gas cylinder valve, you stop the flow of gas into the system, effectively isolating it and minimizing the risk of any further pressure buildup or potential leaks. Once the gas cylinder valve is closed, you can then proceed to investigate and address the underlying cause of the increasing pressure, such as checking for leaks, inspecting the regulator, or seeking professional assistance if necessary.
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Portable electronic machines known as AEDs are used to analyze and treat life-threatening cardiac arrhythmias. They are an automated and external type of a device known as what?
Note that it is correct to state that Portable electronic machines known as AEDs are used to analyze and treat life-threatening cardiac arrhythmias. They are a type of defibrillator.
What is the explanation for the above response?Note that AED's are a kind of defibrillator that are created and designed to be used by laypeople or people of low medical skills instead of medical professionals.
This device can analyze the heart's rhythm and indicated if the patient will need to be shocked with electricity to restore balance to their hearts Rythm.
Thus, it is correct to state that AEDs are an automated and external type of a device known as defibrillator.
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Which of the following is true of the engineering method of separating costs? a. It is generally used to estimate the cost of activities and new products. b. It is sometimes called a time and motion study. c. It separates costs by performing a step-by-step analysis of various elements involved. d. All of these choices are correct.
The engineering method of separating costs is d. All of these choices are correct.
The engineering method of separating costs involves a step-by-step analysis of various elements involved in the production process to estimate the cost of activities and new products.
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Which is the best smartphone in 2022?
Test if a number grade is an A (greater than or equal to 90). If so, print "Great!". Hint: Grades may be decimals. Sample Run Enter a Number: 98.5 Sample Output Great!
Answer:
In Python:
grade = float(input("Enter a Number: "))
if grade >= 90:
print("Great!")
Explanation:
This prompts the user for grade
grade = float(input("Enter a Number: "))
This checks for input greater than or equal to 90
if grade >= 90:
If yes, this prints "Great"
print("Great!")
Strain gage is a device that senses the strain of the structure. The property of the strain gage that is used to correlate with the strain to be measured is
Answer:
resistance
Explanation:
A strain gauge changes resistance with applied strain.
to what potential should you charge a 4.0 μf capacitor to store 4.0 j of energy?
In order to store 4.0 J of energy, a 4.0 μF capacitor should be charged to a potential of 500 V.
The energy stored in a capacitor can be calculated using the formula E = 1/2 * C * V^2, where E is the energy, C is the capacitance, and V is the potential difference across the capacitor. Rearranging the formula, we have V = √(2 * E / C).
Plugging in the values, we get V = √(2 * 4.0 J / 4.0 μF). Simplifying the equation, V = √(2 * 4.0 J / 4.0 * 10^(-6) F) = √(2 * 10^6 V^2) = 2000 V. However, the potential difference is typically given as an absolute value, so the final answer is V = 500 V (assuming positive and negative potentials).
Therefore, the 4.0 μF capacitor should be charged to a potential of 500 V to store 4.0 J of energy.
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1)A wheel is used to turn a valve stem on a water valve. If the wheel radius is 1 foot and the stem, (axle), radius is .5 inches, what is the mechanical advantage of the wheel and axle? 2)How much resistance force can ideally be overcome when an effort of 80 lbs is applied to the wheel of the water valve in problem 1? 3)What is the linear distance traveled when a 2.5' diameter wheel makes one revolution? 4)A compressor motor has a 1.00 inch output shaft (axle) that drives a 4.00inch pulley (wheel). If the motor output shaft supplies 24 lbs of force, ideally how much force does the pulley apply to the drive belt wrapped around it? 5) If the belt pulley's force is measured to be 4 lbs, what is the AMA wheel and axle here?6) What is the efficiency of the compressor motor – belt pulley wheel and axle?
Answer:
for 13
Explanation:
''.''
For one-family dwellings, the service disconnecting means must have a rating of at least ___ amperes, 3-wire.
The rating of the service disconnecting means for a single-family home must be at least 100 amperes, 3-wire.Therefore, 100 amperes is the required minimum rating of service size for a one-family home.
What is the service's required minimum ampere rating?
NEC 230.79 (C) states that the rating of the service disconnecting mechanism for a one-family residence must not be less than 100 amperes, 3-wire.Therefore, 100 amperes is the required minimum rating of service size for a one-family home. In one enclosure, six switches or circuit breakers.Since the 1937 edition of the NEC, the number of switches or sets of circuit breakers that can be utilized as the service disconnecting mechanism to separate a building's premises wiring from the utility provider's conductors can range from one to six. The combined ratings of the circuit breakers, if the disconnecting method consists of more than one switch or circuit breaker, must not be less than the calculated load as established by Art. The 98 amp load for the single-family home will be supplied by a 100 amp electrical service.100 x 83 percent equals 83 amps.The bare minimum service conductor is this one. A revision made to the 2020 NEC mandates that an emergency disconnect be used in accordance with section 230.85.This disconnect is meant to allow emergency personnel to turn off the electricity to the entire house before entering to deal with the situation. Any combination of the following is authorized for the two to six service disconnecting means:separate enclosures, each with a method to disconnect the main service.a main service disconnecting mechanism built inside each panel board enclosure. All primary conductors of transformers that are not grounded must be disconnected using a disconnect.Unless the location of the disconnect is clearly written on the transformer and the disconnect is lockable, as is depicted in the Figure, it must be placed within sight of the transformer.To learn more about ampere rating refer
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Both copper and stainless steel are being considered as a wall material for a liquid cooled rocket nozzle. The cooled exterior of the wall is maintained at 150°C, while the combustion gases within the nozzle are at 2750°C. The gas side heat transfer coefficient is known to be hᵢ = 2×10⁴ W/m²-K, and the radius of the nozzle is much larger than the wall thickness. Thermal limitations dictate that the temperature of copper must not exceed 540°C, while that of the steel must not exceed 980°C. What is the maximum wall thickness that could be employed for each of the two materials? For Cu, ρ = 8933 kg/m³, k = 378 W/m-K and for stainless steel, ρ = 7900 kg/m³, k = 23.2 W/m-K
a. The maximum thickness of the copper nozzle is 3.3 mm
b. The maximum thickness of the steel nozzle is 0.054 mm
The question has to do with heat transfer
What is heat transfer?Heat transfer is the movement of heat energy from one body to anotrher.
How to calculate the maximum wall thickness?Since the rate of heat loss by the gas equal rate of heat gain by the metal.
Rate of heat loss by gasThe rate of heat loss by gas is P = -hA(T - T') where
h = heat transfer coefficient of gas = 2 × 10⁴ W/m²-K, A = surface area of nozzle, T = maximum temperature of metal and T = Temperature of gas = 2750°CRate of heat gain by metalThe rate of heat gain by metal is given by P' = kA(T - T")/t where
k = thermal coefficient of metal, A = surface area of nozzle, T = maximum temperature of metal, T" = temperature of exterior wall of nozzle = 150°C and t = thickness of nozzle. Maximum thickness of nozzle.Since P = P', we have that
-hA(T - T') = kA(T - T")/t
Making t subject of the formula, we have
t = -k(T - T")/h(T - T')
a. Maximum thickness for copper nozzleGiven that for copper
T = 540°C and k = 378 W/m-KSubstituting the values of the variables into t, we have
t = -k(T - T")/h(T - T')
t = -378 W/m-K(540°C - 150°C)/[2 × 10⁴ W/m²-K(540°C - 2750°C)]
t = -378 W/m-K(390°C)/[2 × 10⁴ W/m²-K(-2210°C)]
t = 147420 W/m/4420 × 10⁴ W/m²
t = 147420 W/m/44200000 W/m²
t = 0.0033 m
t = 3.3 mm
So, the maximum thickness of the copper nozzle is 10.71 cm
b. Maximum thickness for steel nozzleGiven that for steel
T = 980°C and k = 23.2 W/m-KSubstituting the values of the variables into t, we have
t = -k(T - T")/h(T - T')
t = -23.2 W/m-K(980°C - 150°C)/[2 × 10⁴ W/m²-K(980°C - 2750°C)]
t = -23.2 W/m-K(830°C)/[2 × 10⁴ W/m²-K(-1770°C)]
t = 19256 W/m/3540 × 10⁴ W/m²
t = 19256 W/m/35400000 W/m²
t = 0.0000544 m
t = 0.0544 mm
t ≅ 0.054 mm
So, the maximum thickness of the steel nozzle is 0.054 mm
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Estimate properties and pipe diameter Determine the diameter of a steel pipe that is to carry 2000 gal/min of gasoline with a pressure drop of 5 psi per 100 ft of horizontal pipe. Pressure drop is a function of flow rate, length, diameter, and roughness. Either iterative methods OR equation solvers are necessary to solve implicit problems. Total head is the sum of the pressure, velocity, and elevation. What is the density of gasoline
Answer:
Diameter of pipe is 0.535 ft
Explanation:
see attachment, its works out 1st half
A substance is malleable, conducts heat, and is used in wiring. How would we classify this substance?.
A substance that is malleable, conducts heat, and is used in wiring would be classified as a metal.
The properties of a substance.In Science, some examples of the mechanical and physical properties of substances used in the construction of buildings include the following:
DensityConductivityResistivityElasticity/stiffnessCorrosionDuctility/malleabilityFractureWhat is conduction?Conduction can be defined as a process which involves the transfer of electric charge or thermal energy due to the movement of particles. Thus, when the conduction relates to electric charge, it is referred to as electrical conduction while when it relates to thermal energy, it is known as heat conduction.
In conclusion, we can infer and logically deduce that a substance that is malleable, conducts heat, and is used in wiring would be classified as a metal.
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A rope is wrapped three and a half times around a cylinder. Determine the range of force T exerted on
the free end of the rope for maintaining equilibrium that is required to just support a 5 kN weight. The
coefficient of friction between the rope and the cylinder is 0.2
The range of force exerted at the end of the rope is; 285.7 N to 1,000 N.
What is the Net horizontal force?The net horizontal force of the cylinder when it is at equilibrium position can be found by applying Newton's second law of motion. Thus;
∑F = 0
F - μF_n = 0
We are given;
F_n = 5 kN = 5000 N
μ = 0.2
Thus;
F - 0.2(5,000) = 0
F - 1,000 = 0
F = 1,000 N
The strength of the applied force will be increasing as the number of turns of the rope increases. Thus;
Minimum force = Total force/number of turns of rope
Since rope is wrapped three and half times, then;
number of turns = 3.5
Thus;
minimum force = 1,000/3.5
minimum force = 285.7 N
Thus, the range of force exerted at the end of the rope is 285.7 N to 1,000 N.
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The rectifier is used to
Answer:
A rectifier is an electrical device used to convert alternating current to direct current.
Explanation:
Hope this helps! Shalom
What component in the solar cell provides electrons to replace the electrons released by the dye?.
The component in the solar cell that provides electrons to replace the electrons released by the dye is "a layer of graphite"
What is the explanation for the above process?A layer of graphite will operate as a counter electrode at the glass/electrolyte border, delivering electrons to the solution to replace these electrons that go on to the FTO glass.
They are reintroduced into the cell on a metal electrode on the rear, commonly known as the counter electrode, after passing through the external circuit and flowing into the electrolyte. The electrons are subsequently returned to the dye molecules by the electrolyte, which regenerates the oxidized dye.
PV cells make use of a variety of semiconductor materials. When exposed to light, the semiconductor absorbs the energy and converts it to negatively charged particles in the material known as electrons. This increased energy permits electrons to flow as an electrical current through the material.
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A certain piece of property is assessed at $150,000. If the tax rate is $2.50 per $100, what is the tax on this property?
Answer:
The tax on this property is \(3750\) dollars
Explanation:
Given
Tax on per $100 is $2.50
Tax on every $1 is \(\frac{2.5}{100} = 0.025\) dollars
Tax on property of value $150,000 is
\(150,000 * 0.025 = 3750\) dollars
The tax on this property is \(3750\) dollars
for a mos transistor biased in the triode region we can define an incremental drain-source resistance as
The incremental drain-source resistance for a MOS transistor biased in the triode region is the ratio of the small change in drain current to the small change in gate voltage and is also dependent on the transistor's channel length, channel width, and oxide thickness.
For a MOS transistor biased in the triode region, the incremental drain-source resistance (also known as the "transconductance") can be defined as the ratio of the small change in drain current to the small change in gate voltage, ΔID/ΔVG. In other words, the transconductance is the change in drain current divided by the change in gate voltage.
The transconductance is also dependent on the transistor's channel length, channel width, and oxide thickness. For a given channel length and width, a longer oxide thickness will result in a lower transconductance, and vice versa. This is because a longer oxide thickness reduces the channel current, which in turn reduces the drain current.
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. There are given three numbers: A, B and C. Even if one of them equal 5 output TRUE, othewise output FALSE.
This can be achieved through a variety of programming languages, here's an example using Python:
A = 4
B = 5
C = 6
if A == 5 or B == 5 or C == 5:
print("TRUE")
else:
print("FALSE")
What is a programming language?A formal language with many instructions is referred to as a programming language. These guidelines are presented to find different outputs. Computer programs are the main use of programming languages. A set of guidelines are presented to ensure the computer's proper operation.
Programming languages are used to control the external devices. In this example, the code checks if any of the variables A, B, or C is equal to 5. If any of them are, the code will output "TRUE", otherwise it will output "FALSE".
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Which of the following units of measurement is denoted by a single apostrophe mark (')?
inch
foot
yard
meter
Answer:
Foot
Explanation:
It is. trust me
inspections may be_____ or limited to a specific area such as electrical or plumbing
A. Metering
B. General
2. A good way to track problems that need to be solved later in the day or
week is with:
A. O Delegating to one person in the group the job of keeping track of everyone's Issues
B. Having each team member write up his or her problems that need solving, and dropping
them in the office suggestion box for later review
C.O A notepad or dry-erase board in the meeting area
D. Having the manager or owner be sure to make a mental note of each problem as it is
discussed, so they can be discussed later
Answer:
C.A notepad or dry-erase board in the meeting area
what are the two basic methods of protecting exterior joints?
1.) Use of sealants—seals the connections between building components. To prevent the infiltration of moisture, air, or other corrosive particles, the joints are sealed. Sealant is a substance that adheres to joint surfaces and hardens into a firm rubbery substance.
2.) The use of prefab coverings, which are often metal and designed to accommodate the joint's anticipated movement. Despite the joints' ability to move, the materials' integrity during assembly should be guaranteed.
Joint sealants play a significant role in the protection of modern commercial facilities against water damage to structures and their contents. While many commercial designs use water-shedding features like lap siding, overlapping flashings, and sloped roofs, many residential structures do not; as a result, there is little to no protection against leaking if a joint sealant fails.
Regrettably, there are several instances during the design and construction process in today's building environment where the poor judgment or inappropriate behavior leads to sealant failure.
For aesthetic and cleanability reasons (on interior surfaces where water resistance is not a concern) as well as to stop sound from traveling through cracks, open joints are sealed using joint sealants (usually interior and internal to composite assemblies).
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graphical forecast for aviation are weather charts best used to
Graphical forecasts for aviation are weather charts that are specifically designed to assist pilots and other aviation professionals in making informed decisions regarding their flights. These forecasts provide a visual representation of current and predicted weather conditions in a specific region, allowing pilots to plan their routes and make adjustments as necessary.
Graphical forecasts are particularly useful because they provide a clear and concise representation of weather patterns that may impact flight operations. By using these charts, pilots can quickly identify areas of potential turbulence, icing, or other weather-related hazards, allowing them to adjust their flight paths or altitude accordingly. Additionally, graphical forecasts are updated frequently, providing pilots with the most up-to-date information available. As a result, pilots can make informed decisions that prioritize safety and ensure a successful flight.
In conclusion, graphical forecasts for aviation are an essential tool that can help pilots navigate complex weather conditions and ensure a safe flight. By providing clear and concise information, these forecasts allow pilots to make informed decisions that prioritize safety and efficiency. As a result, they are an integral part of any flight planning process and should be used by all aviation professionals to ensure a successful flight.
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The feasible region for the pure ILP problem:a. is equivalent to the feasible region for the LP relaxation problemb. is a lattice consisting of points corresponding only to integer values of the decision variablesc. is a k-dimensional hyperspaced. is impossible to determine
It is to be noted that the feasible region for the pure integer linear programming (ILP) problem: " is a lattice consisting of points corresponding only to integer values of the decision variables" (Option B).
What is a Pure Integer Linear Programming problem?An integer programming (IP) issue is a linear programming (LP) problem in which the decision variables must be integers. The goal function as well as the restrictions must be linear. The branch-and-bound approach is the most widely utilized method for solving an IP.
The LP relaxation of an ILP problem is obtained by relaxing the integer constraints on the decision variables, allowing them to take on fractional values.
Thus, the feasible region for the LP relaxation is a superset of the feasible region for the corresponding ILP problem, as it includes all of the points that are feasible for the ILP problem as well as additional points that are feasible for the LP relaxation but not the ILP problem.
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When you hear a radio call that states an aircraft is on the "ILS 3 or RNAV (GPS) 3 approach 5 out", what does this mean and where should you look for traffic? What about "RNAV (GPS) 21 approach 5 out", what does this mean and where should you be looking for traffic? What about "RNAV (GPS) 8 or VOR 8 approach 5 out, what does this mean and where should you look for traffic? What about "RNAV (GPS) 26 approach 5 out", what does this mean and where should
you be looking for traffic?
Answer:
Explanation:
When you hear a radio call that states an aircraft is on the "ILS 3 or RNAV (GPS) 3 approach 5 out", it means that the aircraft is approaching the airport on either the Instrument Landing System (ILS) approach or the Area Navigation (RNAV) approach with a minimum descent altitude of 3,000 feet, and is currently 5 nautical miles away from the airport.
You should look for the aircraft along its expected flight path, which can be found on approach plates or charts provided by the FAA. This information can also be obtained from air traffic control (ATC) if available.
Similarly, when you hear a radio call that states "RNAV (GPS) 21 approach 5 out", it means that the aircraft is approaching the airport on the RNAV (GPS) approach with a minimum descent altitude of 2,100 feet, and is currently 5 nautical miles away from the airport. You should look for the aircraft along its expected flight path.
For "RNAV (GPS) 8 or VOR 8 approach 5 out", it means that the aircraft is approaching the airport on either the RNAV (GPS) approach or the VHF omnidirectional range (VOR) approach with a minimum descent altitude of 800 feet, and is currently 5 nautical miles away from the airport. You should look for the aircraft along its expected flight path.
Finally, for "RNAV (GPS) 26 approach 5 out", it means that the aircraft is approaching the airport on the RNAV (GPS) approach with a minimum descent altitude of 2,600 feet, and is currently 5 nautical miles away from the airport. You should look for the aircraft along its expected flight path.
Consider a receiver with noise power −160 dBm within the signal bandwidth of interest. Assume a simplified path loss model with d0 = 1 m, K obtained from the free space path loss formula with omnidirectional antenna and fc = 1 GHz and gamma = 4. For a transmit power of Pt = 10 mW, find the maximum distance between the transmitter and receiver such that the received signal-to-noise power ratio is 20 dB
As a result, 22.7 metres is the greatest distance between the transmitter and receiver at which the received SNR is 20 dB.
To determine the received power Pr at a distance d from the transmitter with a transmit power of Pt, we can use the following formula: Pr = Pt - PL(d), where PL(d) is equal to K + 10 gamma log10(d/d0).
The following formula can be used to determine the farthest distance dmax at which the received signal-to-noise power ratio (SNR) is 20 dB:
Pr / N0 = SNR
SNR being equal to 20 dB, the formula becomes:
Pr=SNR*N0 = 10
(SNR/10) * N0
In the equation above, we may substitute the equations for Pr and PL(d) to obtain:
Pt-K-Gamma*Log10(d/d0) = 10(SNR/10)*N0
When we solve for d, we obtain: d = d0 * 10
(10 * gamma) / ((Pt - K - SNR * 10 * log10(N0) - 10 * gamma * log10(d0)))
d = 1 * 10^
(10 mW - 20.8 - (-160) - 10*4*log10(1)) / (10*4) = 22.7 metres
As a result, 22.7 metres is the greatest distance between the transmitter and receiver at which the received SNR is 20 dB.
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A legal document that traces the ownership of a piece of property
Answer:
A title
Explanation:
A title is a legal document that proves legal ownership over an asset or piece of property. Assets such as homes, land, other types of real estate, vehicles, and personal property such as jewelry all have titles to demonstrate ownership.
difference between PN junction diode and Bipolar diodes?
PN junction diode and bipolar junction diode are two types of diodes with distinct characteristics and functionalities.
A PN junction diode is a semiconductor device formed by the junction of a p-type region and an n-type region. It operates based on the principle of a PN junction's rectifying behavior, allowing current flow in only one direction. When a forward bias is applied, the diode conducts current, while in reverse bias, it acts as an insulator. PN junction diodes are commonly used for rectification and signal demodulation in electronic circuits.On the other hand, a bipolar junction diode (BJT) consists of three regions: the emitter, base, and collector. It functions as a current-controlled device and can operate in two modes: NPN (negative-positive-negative) and PNP (positive-negative-positive). BJTs are known for their ability to amplify signals and are widely used in applications such as amplifiers, switches, and digital logic circuits.In summary, the main difference between PN junction diode and bipolar junction diode lies in their construction and operating principles. PN junction diodes are based on a single PN junction and primarily used for rectification, while bipolar junction diodes are composed of multiple regions and employed for signal amplification and switching.
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The readings, tA and tB, of two Celsius thermometers, A and B, agree at ice-point (0 oC) and steam point (100 oC), but elsewhere are related by equation tA = l + m tB + n tB 2 where l, m, and n are constants. When both thermometers are immersed in well-stirred oil bath, A registers 51 oC while B registers 50 oC. Determine the reading on B when A reads 25 oC
Answer:
Explanation:
From the case of well-stirred oil bath:
\(51=l+50m+n(50^{2})\rightarrow 51=l+50m+2500n\)
At the ice point, both of the thermometers show the same scale:
\(0 = l + m(0) + n(0^{2}) \rightarrow l = 0\)
At the steam point, again, both of the thermometers show the same scale:
\(100 = 0 + m(100)+n(100^{2}) \rightarrow 100 = 100m + 10000n \rightarrow 1 = m + 100n\)
By eliminating those equations, we find:
\(51=50(1-100n)+2500n \rightarrow 51=50-500n+2500n \rightarrow 1 = 2000n\)
so we can obtain that: \(n=\frac{1}{2000}=0.0005\) and \(m=1-100(0.0005)=1-0.05=0.95\)
Now, we have the complete description of the relation between A and B scale as: \(t_{A}=0.95t_{B}+0.0005t_{B}^{2}\)
So, for \(t_{A}=25^{0}C\):
\(25 = 0.95t_{B}+0.0005t_{B}^{2} \rightarrow 0.0005t_{B}^{2}+0.95t_{B}-25=0\)
\(t_{B}_{1,2}=\frac{-0.95\pm\sqrt{0.95^{2}-4(0.0005)(-25)}}{2(0.0005)}\approx-950\pm975\)
\(t_{B}_{1}=25^{0}C \vee t_{B}_{2}=-1925^{0}C\)