To compute the rate of energy that must be supplied to or removed from the disks to maintain their specified temperatures, we need to consider the radiative heat transfer between the two disks.
The rate of radiative heat transfer between two surfaces can be calculated using the Stefan-Boltzmann law, which states that the rate of heat transfer is proportional to the emissivity of the surfaces, the surface areas, and the temperature difference raised to the fourth power.
In this case, the radiative heat transfer rate between the two disks can be expressed as:
Q = ε1σA1(T1^4 - Tsur^4) + ε2σA2(T2^4 - Tsur^4)
where Q is the heat transfer rate, ε1 and ε2 are the emissivities of the disks (which vary with wavelength), σ is the Stefan-Boltzmann constant, A1 and A2 are the surface areas of the disks facing each other, T1 and T2 are the temperatures of the disks, and Tsur is the temperature of the surroundings.
By substituting the given values of ε1, ε2, A1, A2, T1, T2, and Tsur into the equation, we can calculate the rate of energy that must be supplied to or removed from the disks to maintain their specified temperatures.
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Select four elements to include when considering aesthetics.
Responses
direct costs
direct costs
variety
variety
form
form
emphasis
emphasis
exploded view
exploded view
asymmetry
asymmetry
Aesthetics is a subjective concept that encompasses various elements to create a visually pleasing and harmonious experience. When considering aesthetics, four important elements to include are variety, form, emphasis, and asymmetry.
1. Variety: Incorporating a range of different elements, such as colors, textures, shapes, and patterns, adds visual interest and prevents monotony. Variety can create a dynamic and engaging composition.
2. Form: The form refers to the shape, structure, and overall arrangement of elements. A well-defined and balanced form can evoke a sense of order and unity, contributing to the overall aesthetic appeal.
3. Emphasis: Emphasizing specific elements or focal points draws attention and creates a hierarchy within the composition. This can be achieved through contrasting colors, larger or unique shapes, or strategic placement, enhancing the visual impact.
4. Asymmetry: While symmetry can be visually pleasing, introducing deliberate imbalances or irregularities can add intrigue and uniqueness. Asymmetry creates a sense of movement and visual tension, making the design more captivating.
By considering these four elements, one can create a visually appealing aesthetic that is diverse, well-structured, visually engaging, and aesthetically intriguing.
Remember that these elements can be applied differently based on the context and desired outcome, allowing for endless possibilities and creative expressions.
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Why do the quadrants in coordinate plane go anti-clockwise?.
Answer:
Quadrants are counter-clockwise because angles are measured counter-clockwise; and angles are measured counter-clockwise so that Cross Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin).
Explanation:
Dimensional analysis suggests that the drag of the car can be [2] expressed as a non-dimensional functional relationship of the form
D/0.5pwhv^2 = function(p/µvh)
The dimensional analysis suggests that the drag of the car can be related to the non-dimensional parameters p/µvh through a functional relationship, allowing for the prediction and understanding of the drag forces experienced by the car.
Dimensional analysis suggests that the drag of the car can be expressed as a non-dimensional functional relationship of the form:
D/0.5pwhv² = f(p/µvh)
where:
D is the drag force,
p is the fluid density,
w is a characteristic width,
h is a characteristic height,
v is the velocity of the car,
µ is the dynamic viscosity of the fluid, and
f is a dimensionless function.
In this relationship, the left-hand side represents the non-dimensional drag force, which is the ratio of the drag force to the dynamic pressure of the fluid. The right-hand side is a non-dimensional term that depends on the non-dimensional parameters p/µvh, representing the ratio of the fluid density, dynamic viscosity, characteristic velocity, and characteristic length.
The specific form of the function f depends on the specific characteristics and geometry of the car, as well as the flow conditions and fluid properties. Through experimentation and analysis, the function f can be determined or approximated for a given car and flow conditions.
Overall, the dimensional analysis suggests that the drag of the car can be related to the non-dimensional parameters p/µvh through a functional relationship, allowing for the prediction and understanding of the drag forces experienced by the car.
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Heat is to be transferred from water to air through an aluminum wall. It is proposed to add rectangular fins 0.05 in. thick and 3/4 in. long spaced 0.08 in. apart to the aluminum surface to aid in transferring heat. The heat-transfer coefficients on the air and water sides are 3 and 25 Btu/h ft2 oF, respectively. Evaluate the percent increase in heat transfer if these fins are added to (a) the air side, (b) the water side, (c) and both sides. What conclusions may be reached regarding this result
In the circuit given below, R1 = 17 kΩ, R2 = 74 kΩ, and R3 = 5 MΩ. Calculate the gain 1formula58.mml when the switch is in position 1, position 2, and position 3.
A) The gain 1formula58.mml at the position 1 is _____.
B) The gain 1formula58.mml at the position 2 is _____.
C) The gain 1formula58.mml at the position 3 is _____.
Answer:a
a) Vo/Vi = - 3.4
b) Vo/Vi = - 14.8
c) Vo/Vi = - 1000
Explanation:
a)
R1 = 17kΩ
for ideal op-amp
Va≈Vb=0 so Va=0
(Va - Vi)/5kΩ + (Va -Vo)/17kΩ = 0
sin we know Va≈Vb=0
so
-Vi/5kΩ + -Vo/17kΩ = 0
Vo/Vi = - 17k/5k
Vo/Vi = -3.4
║Vo/Vi ║ = 3.4 ( negative sign phase inversion)
b)
R2 = 74kΩ
for ideal op-amp
Va≈Vb=0 so Va=0
so
(Va-Vi)/5kΩ + (Va-Vo)74kΩ = 0
-Vi/5kΩ + -Vo/74kΩ = 0
Vo/Vi = - 74kΩ/5kΩ
Vo/Vi = - 14.8
║Vo/Vi ║ = 14.8 ( negative sign phase inversion)
c)
Also for ideal op-amp
Va≈Vb=0 so Va=0
Now for position 3 we apply nodal analysis we got at position 1
(Va - Vi)/5kΩ + (Va - Vo)/5000kΩ = 0 ( 5MΩ = 5000kΩ )
so
-Vi/5kΩ + -Vo/5000kΩ = 0
Vo/Vi = - 5000kΩ/5kΩ
Vo/Vi = - 1000
║Vo/Vi ║ = 1000 ( negative sign phase inversion)
When making an airborne VOR check, what is the maximum allowable tolerance between the two indicators of a dual VOR system (units independent of each other except the antenna)
When performing an airborne VOR (VHF Omnidirectional Range) check, the maximum allowable tolerance between the two indicators of a dual VOR system is typically defined by aviation regulations and guidelines.
Specifically, in the United States, the Federal Aviation Administration (FAA) provides guidance on VOR equipment tolerances and requirements.
According to FAA regulations, the maximum allowable tolerance for a dual VOR system is ±4° or ±6°, depending on the specific situation.
For enroute and terminal operations, the maximum allowable tolerance is ±4°.
This means that the indications on the two VOR indicators can differ by up to 4° without being considered a significant deviation.
For non-precision approaches, such as VOR approaches, the maximum allowable tolerance is ±6°.
This provides a slightly wider tolerance to account for the increased precision required during approach procedures.
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Which step in the reverse-engineering process involves the identification of subsystems and their relationship to one another?
The answer is analyze
One - tenth kilogram of air as an ideal gas with k= 1.4 executes a carnot refrigeration cycle as shown i fig. 5,16, the isothermal expansion occurs at - 23C with a heat transfer to the air of 3.4 kj. The isothermal compression occurs at 27C to a final volume of 0.01m. Using the results of prob. 5.80 adapted to the case, Determine (a) the pressure, in Kpa, at each of the four principal states (b) the work, in KJ for each of the four processes (c) the coefficient of performance
Answer:
Hello your question is incomplete attached below is the missing part
a) p1 = 454.83 kPa, p2 = 283.359 Kpa , p3 = 536.423 kpa , p4 = 860.959kPa
b) W12 = 3.4 kJ, W23 = -3.5875 KJ, W34 = -4.0735 KJ, W41 = 3.5875 KJ
c) 5
Explanation:
Given data:
mass of air ( m ) = 1/10 kg
adiabatic index ( k ) = 1.4
temperature for isothermal expansion = 250K
rate of heat transfer ( Q12 ) = 3.4 KJ
temperature for Isothermal compression ( T4 ) = 300k
final volume ( V4 ) = 0.01m ^3
a) Calculate the pressure, in Kpa, at each of the four principal states
from an ideal gas equation
P4V4 = mRT4 ( input values above )
hence P4 = 860.959kPa
attached below is the detailed solution
b) Calculate work done for each processes
attached below is the detailed solution
C) Calculate the coefficient of performance
attached below is detailed solution
A 1.78-m3 rigid tank contains steam at 220°C. One-third of the volume is in the liquid phase and the rest is in the vapor form. The properties of steam at 220°C are given as follows: vf = 0.001190 m3/kg and vg = 0.08609 m3/kg.
determine the density
The tank has a total volume of 1.78 m3, of which one third is in the liquid phase, and the remaining two thirds are in the vapour phase. The system has a density of 287.6 kg/m3.
Describe density.Density is the measurement of how tightly a substance is packed. It has such definition since it is the mass per unit volume. The density symbol is D, and the density formula is The formula is: = m/V when is the density, m is the object's mass, and V is its volume.
Volume of vapor = (2/3) x 1.78 = 1.1867 m^3
Volume of liquid = (1/3) x 1.78 = 0.5933 m^3
To determine the density, we need to find the mass of the vapor and the mass of the liquid..
Mass of vapor = Volume of vapor / Specific volume of vapor = 1.1867 m^3 / 0.08609 m^3/kg = 13.785 kg
Mass of liquid = Volume of liquid / Specific volume of liquid = 0.5933 m^3 / 0.001190 m^3/kg = 498.3 kg
The total mass of the system is the sum of the mass of the vapor and the mass of the liquid:
Total mass = Mass of vapor + Mass of liquid = 13.785 kg + 498.3 kg = 512.085 kg
Finally, we can calculate the density using the total mass and the total volume of the system:
Density = Total mass / Total volume = 512.085 kg / 1.78 m^3 = 287.6 kg/m^3
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The angle of attack of a wing directly controls the A) angle of incidence of the wing. B) amount of airflow above and below the wing. C) distribution of pressures acting on the wing.
The angle of attack of a wing directly controls the C) distribution of pressures acting on the wing.
When the angle of attack of a wing is increased, the air moving over the curved upper surface of the wing must travel a greater distance and faster than the air moving beneath the wing's flat lower surface. This creates an area of lower air pressure above the wing and an area of higher air pressure beneath the wing, resulting in lift. The greater the angle of attack, the greater the lift produced.
However, if the angle of attack is too great, the airflow over the wing may separate, causing a loss of lift and potentially leading to a stall. Therefore, proper control of the angle of attack is crucial for safe and efficient flight.
Option C is answer.
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An iron-constantan thermocouple is to be used to measure temperatures between 0and 400 degree C. What will be the non-linearity error as a percentage of the full-scale reading at 100 degree C If a linear relationship is assumed between e.m.f and temperature? E.M.F at 100 degree C= 5.268 m V; e.m.f at 400 degree C= 21.846 m V
The non-linearity error as a percentage of the full-scale reading at 100 degree C is - 0.89%.
What is non-linearity error?Non-linearity error is defined as the biggest deviation from a straight line linking the output signal to the applied force, known as the "best straight," that the calibration curve makes. In order to eliminate second order nonlinearity, the sensor signal conditioning system feeds a portion of the output signal back to the sensor.
If EMF and Celsius temperature have a proportional relationship, then the recorded value of EMF at 100 °C will be understood to be a temperature of.
T/5.268 = 400/21.846
T = 5.268(400/21.846) ≈ 96.457 °C
As a percentage of the full scale, the mistake is
(96.457 -100)/400 × 100% ≈ -0.886%
Thus, the non-linearity error as a percentage of the full-scale reading at 100 degree C is - 0.89%.
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Calculate the maximum bit rate for each of the following Modulation and Coding Schemes (MCS) if the signaling bandwidth is 20MHz.
The maximum bit rate for each MCS depends on the specific modulation and coding scheme used.
What is the maximum bit rate for each Modulation and Coding Scheme (MCS) with a signaling bandwidth of 20MHz?To calculate the maximum bit rate for each Modulation and Coding Scheme (MCS) with a signaling bandwidth of 20MHz, we need to consider the modulation scheme and coding rate for each MCS.
MCS is typically used in wireless communication systems. The maximum bit rate depends on the number of bits per symbol (modulation order) and the coding rate (efficiency).
For example, if MCS 8 uses 256-QAM modulation and a coding rate of 3/4, the maximum bit rate can be calculated as follows: Bit rate = signaling bandwidth ˣ modulation order ˣ coding rate = 20MHz ˣ log2(256) ˣ (3/4) = 20MHz ˣ 8 ˣ (3/4) = 120Mbps.
By applying similar calculations for each MCS, we can determine the maximum bit rate for each specific modulation and coding combination.
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The southbound interface provides a uniform means for application developers and network managers to access SDN services and perform network management tasks.
Why this statement is false?
No, the southbound interface in SDN is not responsible for providing a uniform means for application developers and network managers to access SDN services and perform network management tasks.
Is the southbound interface in SDN responsible for providing a uniform?The statement is false because the southbound interface in Software-Defined Networking (SDN) is not responsible for providing a uniform means for application developers and network managers to access SDN services and perform network management tasks.
The southbound interface is the interface between the SDN controller and the network devices (switches, routers) and is responsible for transmitting control instructions and forwarding policies from the controller to the network devices. It is focused on communication and control between the controller and the network infrastructure.
The northbound interface, on the other hand, is responsible for providing a uniform means for application developers and network managers to access SDN services and perform network management tasks by allowing them to interact with the SDN controller.
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1. types of ecosystem ?
2. explain each ecosystem
Determine the minimum required wire radius assuming a factor of safety of 3 and a yield strength of 1500 MPa.
This question is incomplete, the complete question is;
A large tower is to be supported by a series of steel wires. It is estimated that the load on each wire will be 11,100 N.
Determine the minimum required wire radius assuming a factor of safety of 3 and a yield strength of 1500 MPa.
answer in mm please
Answer:
the minimum required wire radius is 5.3166 mm
Explanation:
Given that;
Load F = 11100N
N = 3
∝y = 1500 MPa
∝workmg = ∝y / N = 1500 / 3 = 500 MPa
now stress of Wire:
∝w = F/A
500 × 10⁶ = 11100 / A
A = 22.2 × 10⁻⁶ m²
so
(π/4)d² = A
(π/4)d² = 22.2 × 10⁻⁶
d² = 2.8265 × 10⁻⁵
d = 5.3165 7 × 10⁻³ m³
now we convert to mm(millimeters)
d = 5.3166 mm
Therefore the minimum required wire radius is 5.3166 mm
unitate de masura in SI pt F
Answer:
Electrical Capacitance
Explanation:
To find - unit of measure in SI for F
Solution -
The answer is - Electrical Capacitance
Reason -
The farad (symbol: F) is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge.
Răspuns:
Capacitate electrică
Explicaţie:
Pentru a găsi - unitate de măsură în SI pentru F
Soluție -
Răspunsul este - Capacitate electrică
Motiv -
Farada (simbolul: F) este unitatea de capacitate electrică derivată din SI, capacitatea unui corp de a stoca o sarcină electrică.
What is the relationship of VMO and MMO, in a climb and descent?A) If climbing at VMO, it is possible to exceed MMO. B) If descending at MMO, VMO cannot be exceeded. C) If climbing at VMO, Mach number is decreasing. D) If climbing at MMO, Indicated Airspeed is increasing
A) If climbing at VMO, it is possible to exceed MMO.VMO and MMO are two different limits that aircraft have to operate within to ensure their safety.
VMO is the maximum indicated airspeed at which the aircraft can be flown without risking damage to the structure due to excessive aerodynamic loads. On the other hand, MMO is the maximum Mach number at which the aircraft can be flown without risking the onset of compressibility effects, such as shock waves and control surface flutter.During a climb, the airspeed decreases as the aircraft gains altitude, while the Mach number increases due to the decreasing air density. Therefore, if an aircraft is climbing at VMO, it is possible to exceed MMO since the Mach number is increasing while the airspeed is decreasing.
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A cylindrical rod of copper (E = 110 GPa) having a yield strength of 240 MPa is to be subjected
to a load of 6660 N. If the length of the rod is 380 mm, what must be the diameter to allow an
elongation of 0.50 mm?
Answer:
"7.654 mm" is the correct solution.
Explanation:
According to the question,
\(E=110\times 10^3 \ N/mm^2\)\(\sigma_y = 240 \ mPa\)\(P = 6660 \ N\)\(L = 380 \ mm\)\(\delta = 0.5 \ mm\)Now,
As we know,
The Elongation,
⇒ \(E=\frac{\sigma}{e}\)
\(=\frac{\frac{P}{A} }{\frac{\delta}{L} }\)
or,
⇒ \(\delta=\frac{PL}{AE}\)
By substituting the values, we get
\(0.5=\frac{6660\times 380}{(\frac{\pi}{4}D^2)(110\times 10^3)}\)
then,
⇒ \(D^2=58.587\)
\(D=\sqrt{58.587}\)
\(=7.654 \ mm\)
Consider the following three-level NOR circuit: (a) Find all hazards in this circuit. (b) Redesign the circuit as a three-level NOR circuit that is free of all hazards
(a) The hazards in this circuit are:
Stuck-at-0 hazard: when all inputs are 0, the output is stuck at 0.Stuck-at-1 hazard: when all inputs are 1, the output is stuck at 1.(b) The redesigned three-level NOR circuit should look like this:
A B C | Y 0 0 0 | 1 0 0 1 | 0 0 1 0 | 0 0 1 1 | 0 1 0 0 | 0 1 0 1 | 0 1 1 0 | 0 1 1 1 | 0
A parachute is essential for skydiving because it helps to slow the skydiver's descent and creates a more stable aerodynamic shape in the air. This helps to reduce the risk of injury or death due to the skydiver spinning out of control.
Additionally, the parachute's canopy helps to reduce oscillations, providing a more balanced descent. This is especially important when skydiving in areas with high winds that could otherwise cause the skydiver to be thrown off course. The parachute also creates a larger surface area for the air to flow through, increasing the drag and slowing the skydiver's descent. Ultimately, the parachute helps to ensure a safe and controlled skydive.
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suppose we have an application that requires power outage probability of 0.01 for the threshold p0=-80dbm .for rayleigh fading ,what value of the average signalpoweris required
To find the value of the average signal power required for a power outage probability of 0.01 for a threshold of p0 = -80dBm, we need to use the Rayleigh fading model, which describes the statistical distribution of signal strength in a wireless communication channel.
The Rayleigh fading model assumes that the magnitude of the received signal power follows a Rayleigh distribution, which is a continuous probability distribution with a scale parameter σ. The probability density function of the Rayleigh distribution is given by:
f(x) = (x/σ^2) * exp(-x^2/(2σ^2))
where x is the signal power, and σ is the scale parameter, which is related to the average signal power P as follows:
σ = sqrt(P/2)
The power outage probability for a given threshold p0 is given by:
Pout = exp(-2*(p0/P))
where Pout is the power outage probability.
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PLEASE HELP give an example of how scientists, technologists, engineers, and mathematicians may work together when inventing or innovating a new product. Include the role of each profession.
An example of them working together would be something like building a robot. Technologists would work on this project bc they would code the robot. Engineers would work on this bc they would design the interior. A mathematician would work in this bc a mathematician would calculate the angels of when a robot picks something up or when it turns. A scientist would work on this bc the scientist know about physics. You need physics so u know how much force to apply, how much energy to use, how much mass u need, and how much charge u need.
Explanation:
the most notable aspect in managing C/N for downlink designs is
Answer:
Explanation:
In satellite communications, downlink is the establishment of a communications link from an orbiting satellite down to one or more ground stations on Earth. Contrast with uplink.
_____________ 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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Use the body of a persuasive request to gain your reader's attention and interest. Group of answer choices True False
The given statement "Use the body of a persuasive request to gain your reader's attention and interest" is true because the body of a persuasive request plays a crucial role in capturing the reader's attention and interest.
Does the body of a persuasive request grab attention?When crafting a persuasive request, it is crucial to make a compelling case that captivates your reader right from the start. The body of the request should be structured in a way that engages the reader, presenting a clear and persuasive argument that addresses their needs or concerns. By using persuasive language, appealing to emotions, providing evidence, and demonstrating the benefits or value, you can effectively gain your reader's attention and interest.
Additionally, utilizing storytelling techniques, personal anecdotes, or relevant examples can make your request more relatable and memorable. Ultimately, a well-crafted body of a persuasive request can significantly increase the likelihood of your reader responding positively to your appeal.
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Python Programming Questions 1. Software Sales (see Chapter 3, Programming Exercises 12) from the textbook Starting out with Python Fourth Edition by Tony Gaddis: A software company sells a package that retails for $125. Quantity discounts are given according to the following table: Quantity Discount 10-19 5% 20-49 15% 50-99 20%
100 or more 30% Provide a Python program that asks the user to enter the number of packages purchased. The program should then display the number of packages purchased, the amount of the discount (if any) and the total amount of the purchase after the discount. Submit: Algorithm, Python code with documentation, Output. Please explain the Algorithm and this is just a normal program not a function.
This is what I have done I was suppose to just provide a normal program but instead I did it in function.
def purchase_package(quantity):
price = 125
quantity_discount = 0;
# assign discount based on package quantity
if (quantity >=10 and quantity < 20):
quantity_discount = 0.05
elif (quantity >= 20 and quantity < 50):
quantity_discount = 0.15
elif (quantity >= 50 and quantity < 100):
quantity_discount = 0.20
elif (quantity >= 100):
quantity_discount = 0.30
# calculate the total amount after discount total_amount = quantity * price - (quantity * price * quantity_discount)
# display the number of packages purchased, the amount of the discount (if any) a # and the total amount of the purchase after the discount.
print("Total Number of packages purchased: ", quantity);
if (quantity_discount > 0):
print("Discount: {quantity_discount * 100}%");
print("Total amount: ", total_amount);
# Ask for user input, will keep asking for input until it is a valid number
while(True):
quantity = input("Enter number of package/s: ")
try:
quantity = int(quantity)
if (quantity >= 1):
purchase_package(quantity)
break;
else:
print("Please Input a Valid Number!!")
except ValueError:
print("Please Input a Valid Number!!")
The program starts by asking the user to enter the number of packages purchased. Below is the algorithm and programming code part of the given problem in python.
Algorithm of the given problem:
Get the number of packages purchased from the userCheck the quantity purchased and calculate the discount according to the tableCalculate the total amount of the purchase after the discountDisplay the number of packages purchased, the amount of the discount, and the total amount of the purchasePython code with documentation:
# Get the number of packages purchased from the user
num_of_packages = int(input("Enter the number of packages purchased: "))
# Set initial values for discount and total
discount = 0
total = num_of_packages * 125
# Check the quantity purchased and calculate the discount according to the table
if num_of_packages >= 10 and num_of_packages <= 19:
discount = total * 0.05
elif num_of_packages >= 20 and num_of_packages <= 49:
discount = total * 0.15
elif num_of_packages >= 50 and num_of_packages <= 99:
discount = total * 0.2
elif num_of_packages >= 100:
discount = total * 0.3
# Calculate the total amount of the purchase after the discount
total -= discount
# Display the number of packages purchased, the amount of the discount, and the total amount of the purchase
print("Number of packages purchased: ", num_of_packages)
print("Discount amount: $" + str(discount))
print("Total amount of purchase: $" + str(total))
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When an electric current flows through a wire with resistance, energy is a. liberated as x-rays b. liberated as heat c. liberated as light
When an electric current flows through a wire with resistance, energy is liberated as heat.
Thus, when a current flows through the resistor, the electrical energy is converted into heat energy. Hence the heat that is generated in the components of the circuit possesses some resistance and is dissipated into the air around the components.
Resistance in a wire causes a hindrance to the flow of electrons, which results in the conversion of electrical energy into thermal energy. This thermal energy is then dissipated into the surrounding environment, which can be felt as heat.
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A converging nozzle has an exit area of 0.001 m2. Air enters the nozzle with negligible velocity at a pressure of 1 MPa and a temperature of 360 K. For isentropic flow of an ideal gas with k = 1.4 and the gas constant R = Ru/MW = 287 J/kg-K, determine the mass flow rate in kg/s and the exit Mach number for back pressures of (a) 500 kPa and (b) 784 kPa.
Answer:
a) for back pressures of (a) 500 kPa
- mass flow rate is 2.127 kg/s
- exit Mach number is 1.046
b) for back pressures of (a) 784 kPa
- mass flow rate is 1.793 kg/s
- exit Mach number is 0.6
Explanation:
Given that;
A₂ = 0.001 m²
P₁ = 1 MPa
T₁ = 360 K
k = 1.4
P₂ = 500 Kpa
(1000/500)^(1.4-1 / 1.4) = 360 /T₂
2^(0.4/1.4) = 360/T₂
1.219 = 360 / T₂
T₂ = 360 / 1.219
T₂ = 295.32 K
CpT₁ + V₁²/2000 = CpT₂ + V₂²/2000
we substitute
CpT₁ + V₁²/2000 = CpT₂ + V₂²/2000
1.005 × 360 = 1.005 × 295.32 + v₂²/2000
v₂ = 360.56 m/s²
p₂v₂ = mRT₂
500 × (0.001 × 360.56) = m × 0.287 × 295.32
m = 2.127 kg/s
so Mach Number = V₂ / Vc
Vc = √( kRT) = √( 1.4 × 287 × 295.32) = 344.47 m/s
So Mach Number = V₂ / Vc = 360.56 / 344.47 = 1.046
Therefore for back pressures of (a) 500 kPa
- mass flow rate is 2.127 kg/s
- exit Mach number is 1.046
b)
AT P₂ = 784 kPa
(1000/784)^(1.4-1 / 1.4) = 360/T₂
T₂ = 335.82 K
now
V₂²/2000 = 1.005( 360 - 335.82)
V₂ = 220.45 m/s
P₂V₂ = mRT₂
784 × (0.001 × 220.45) = m( 0.287) ( 335.82)
172.83 = 96.38 m
m = 172.83 / 96.38
m = 1.793 kg/s
just like in a)
Vc = √( kRT) = √( 1.4 × 287 × 335.82) = 367.32 m/s
Mach Number = V₂ / Vc = 220.45 / 367.32 = 0.6
Therefore for back pressures of (a) 784 kPa
- mass flow rate is 1.793 kg/s
- exit Mach number is 0.6
Following are the
Given:
\(A_2 = 0.001\ m^2\\\\P_1 = 1\ MPa\\\\T_1 = 360\ K\\\\k = 1.4\\\\P_2 = 500\ Kpa\\\\\)
To find:
Flow rate of mass, and Mach number
Solution:
For point a)
Using formula:
\(\to P^{\frac{r-1}{r}} \alpha T\\\\\to (\frac{1000}{500})^(\frac{1.4-1}{1.4}) = \frac{360}{T_2}\\\\\to 2^(\frac{0.4}{1.4}) = \frac{360}{T_2}\\\\\to 1.219 = \frac{360}{T_2}\\\\\to T_2 = \frac{360}{1.219}\\\\\to T_2 = 295.32\ K\\\\\)
\(\to C_pT_1 + \frac{V_1^2}{2000} = C_pT_2 + \frac{V_2^2}{2000}\\\\\to 1.005 \times 360 = 1.005 \times 295.32 + \frac{v_2^2}{2000}\\\\\to v_2 = 360.56 \ \frac{m}{s^2} \\\\\to p_2v_2 = mRT_2\\\\\to 500 \times (0.001 \times 360.56) = m \times 0.287 \times 295.32\\\\\to m = 2.127\ \frac{kg}{s}\\\\\)
Mach Number \(= \frac{V_2}{V_c}\\\\\)
\(\to V_c = \sqrt{( kRT)} = \sqrt{( 1.4 \times 287 \times 295.32)} = 344.47 \ \frac{m}{s}\\\\\)
\(\to \frac{V_2}{V_c} = \frac{360.56}{344.47} = 1.046\)
For point b)
\(\to P_2 = 784\ kPa\\\\\to (\frac{1000}{784})^{(\frac{0.4}{1.4})} = \frac{360}{T_2}\\\\\to T_2 = 335.82\ K\\\\\)
now
\(\to \frac{V_2^2}{2000} = 1.005( 360 - 335.82)\\\\\to V_2 = 220.45 \frac{m}{s}\\\\\to V_c = \sqrt{( kRT)} = \sqrt{( 1.4 \times 287 \times 335.82)} = 367.32\ \frac{ m}{s}\\\\\to c= \frac{220.45}{ 367.32} = 0.6\\\)
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Consider the string length equal to 7. This string is distorted by a function f (x) = 2 sin(2x) - 10sin(10x). What is the wave formed in this string? a. In=12cos (nit ) sin(max) b. 2cos(2t)sin (2x) - 10cos(10t ) sin(10x) c. n 2 sin 2x e' – 10sin 10x e
Answer:
hello your question has a missing part below is the missing part
Consider the string length equal to \(\pi\)
answer : 2cos(2t) sin(2x) - 10cos(10t)sin(10x)
Explanation:
Given string length = \(\pi\)
distorted function f(x) = 2sin(2x) - 10sin(10x)
Determine the wave formed in the string
attached below is a detailed solution of the problem
how did hubble show that the andromeda galaxy was, in fact, a distant galaxy?
In 1923, astronomer Edwin Hubble used the 100-inch telescope at the Mount Wilson Observatory to observe Cepheid variable stars in the Andromeda galaxy.
Cepheid variable stars are stars whose brightness fluctuates regularly, and their brightness is directly related to their period of variability. By measuring the period of variability of the Cepheid variables in Andromeda, Hubble was able to determine their intrinsic brightness, or absolute magnitude. He then compared this to their apparent brightness as seen from Earth and found that they were much fainter than expected if Andromeda was a nearby object in our own galaxy. Hubble concluded that the only explanation for the faintness of the Cepheid variables was that Andromeda was actually a separate galaxy far beyond the Milky Way, and not a nearby nebula as previously thought. This discovery provided evidence for the concept of an expanding universe and helped establish the field of extragalactic astronomy. It also led to the realization that there were many other galaxies beyond the Milky Way, and that the universe was much larger than previously thought.
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Answer:
He observed Cepheid variables in the galaxy
Explanation:
acetone flows at a volume flow rate of 50 gpm through a 2 nominal schedule 40 commercial steel pipe. the pipe is laid out horizontally and is 50 ft long. calculate the pressure drop.
Explanation:
The pressure drop can be calculated using the Darcy-Weisbach equation:
ΔP = (f * L * V^2) / (2 * g * D)
where:
ΔP = Pressure drop (psi)
f = Darcy friction factor
L = Length of pipe (ft)
V = Velocity of fluid (ft/s)
g = acceleration due to gravity (32.2 ft/s^2)
D = Inner diameter of pipe (ft)
To calculate the velocity, use the equation:
V = Q / A
where:
V = Velocity (ft/s)
Q = volumetric flow rate (ft^3/s)
A = cross-sectional area of pipe (ft^2)
To convert volumetric flow rate from gpm to ft^3/s:
Q = 50 gpm * 0.002228 ft^3/s/gpm
The diameter of the 2" Schedule 40 commercial steel pipe can be found from pipe dimensions charts and is approximately 0.154 ft.
The cross-sectional area can be calculated as:
A = π * (D/2)^2
Plugging in the values:
V = (50 * 0.002228) / (π * (0.154/2)^2) = 24.7 ft/s
ΔP = (f * 50 * 24.7^2) / (2 * 32.2 * 0.154)
The value of the friction factor, f, can be estimated using the Moody diagram or calculated using a more complex equation such as the Colebrook-White equation.
Note: This is a simplified calculation and does not account for all factors that could affect pressure drop such as changes in pipe elevation, fittings, and valves.