Calculate the power in Watts) in one sideband of an AM signal whose carrier power is 86 Watts. The unmodulated current is 1.52 A while the modulated current is 1.75 A. No need for a solution. Just write your numeric answer in the space provided. Round off your answer to 2 decimal places.
Answers
The power in one sideband of an AM (amplitude modulation) signal can be calculated using the formula:
Psb = (Ic^2 - Iu^2) / 2
where Psb is the power in one sideband, Ic is the modulated current, and Iu is the unmodulated current.
In this case, the unmodulated current (Iu) is given as 1.52 A and the modulated current (Ic) is given as 1.75 A. We can substitute these values into the formula:
Psb = (1.75^2 - 1.52^2) / 2
Calculating the values inside the brackets:
(1.75^2 - 1.52^2) = (3.0625 - 2.3104) = 0.7521
Dividing this by 2:
0.7521 / 2 = 0.37605
Rounding off the answer to 2 decimal places, we get:
Psb ≈ 0.38 Watts
Therefore, the power in one sideband of the AM signal is approximately 0.38 Watts.
The power in one sideband of the AM signal with a carrier power of 86 Watts, an unmodulated current of 1.52 A, and a modulated current of 1.75 A is approximately 0.38 Watts.
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Related Questions
What historic event / period marked the beginning of the manufacturing boom in the mid-
to-late 18th century (1700s)?
Answers
Answer:
Industrial revolution too bad at english languge not fleunt so if say a whole story of this i will not make secene but answer is to it industrial revolution.
Explanation:
Given is the binary search and answer the following 70 a. Find the height of the tree with root 70. (1 points) b. Find the height of the tree with root 70. (1 points) C. List the path from the node with info 92 to the node with info 78. (1 points) d. A node with info 30 is to be inserted in the tree. List the nodes that are visited by the function insert to insert 30. Redraw the tree after inserting 30. What is the height of the tree after inserting 30? (2 points) e. Delete node 45 and redraw the binary tree. What is the height of the tree after deleting 45? (2 points) f. Delete nodes 63 and 82 in that order. Redraw the binary tree after each deletion. What is the height of the tree after deleting 63 and 82? (2 points) g. Delete node 70 and redraw the binary tree. What is the height of the tree after deleting 70? (2 points) 2. Insert 28, 25, 26, 42, 47, 30, 45, 29, 5 into an initially empty binary search tree. Draw the final binary search tree.
Answers
a. The height of a tree is the maximum number of edges in any path from the root to a leaf node. To find the height of the tree with root 70, we need to traverse the tree and determine the longest path from the root to a leaf. The height of the tree is the length of that path.
b. To find the height of the tree with root 70, we need to traverse the tree and determine the longest path from the root to a leaf. The height of the tree is the length of that path.
c. To list the path from the node with info 92 to the node with info 78, we start from the root and traverse the tree following the appropriate branches at each node until we reach the target node. We record the nodes visited during this traversal to obtain the path from node 92 to node 78.
d. To insert a node with info 30 in the binary search tree, we start at the root and compare the values until we find the appropriate position for insertion. The nodes visited during this process are the nodes that are traversed to insert the node with info 30. After inserting 30, we redraw the tree and determine its height.
e. To delete node 45 from the binary search tree, we need to find the node and rearrange the tree accordingly. After deleting 45, we redraw the tree and determine its height.
f. To delete nodes 63 and 82 from the binary search tree, we need to find the nodes and rearrange the tree accordingly. We perform the deletions in the specified order, redrawing the tree after each deletion. After deleting both nodes, we determine the height of the resulting tree.
g. To delete node 70 from the binary search tree, we need to find the node and rearrange the tree accordingly. After deleting 70, we redraw the tree and determine its height.
In conclusion, by following the instructions given and performing the required operations on the binary search tree, we can find the heights of the tree in different scenarios and draw the resulting trees.
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Which of the following will create a screen object? Python
screen = turtle()
screen = turtle.Screen()
screen = screen.Turtle()
screen = turtle.Turtle()
Answers
Answer:
what?
Explanation:
One signal vin=0.2sin(wt) is applied to a bridge rectifier where Silicon diodes are used. The peak value of output voltage is expected to be
a)can't be estimated due to insufficient data
b)0.0
c)0.2
d)0.4
Answers
Answer:
This problem has been solved!
See the answer
7. The voltage that must be less than the breakdown voltage of the diode in order to prevent damage to the diode is the ________.
peak inverse voltage
maximum diode voltage
reverse surge voltage
maximum peak voltage
8. Assume the input signal to a rectifier circuit has a peak value of Vm = 12 V and is at a frequency of 60 Hz. Assume the output load resistance is R = 2kΩ and the ripple voltage is to be limited to Vr= 0.4 V. Determine the capacitance required to yield this specification for a (a) full-wave rectifier and (b) half-wave rectifier. Show all work.
9.A full-wave rectifier is to be designed to produce a peak output voltage of 12 V, deliver 120 mA to the load, and produce an output with a ripple of not more than 5 percent. An input line voltage of 120 V (rms), 60 Hz is available. Consider a bridge type rectifier. Specify the transformer ratio and the size of the required filter capacitor. Show all work.
Explanation:
water (10 oc) flows with a speed of 2 m/s through a horizontal run of pvc pipe. the length of the pipe is 50 m, and the pipe is schedule 40 with a nominal diameter of 2.5 inch. calculate: a) the pressure drop in kpa b) the head loss in meters c) the power in watts needed to overcome the head loss
Answers
The pipe is schedule 40 and has a nominal diameter of 2.5 inches. It is 50 meters long. Then pressure drop is 29.1kpa,Head loss is 2.967m and power is 176.986 watt.
a)Pressure drop = 32μVL/D²
=32*1.307*10⁻³*2*50/0.0119882
=29102.6 pascal
=29.1 Kpa
b)Head loss=p1-p2/pg=29.1*10³/999.7*9.81
=2.967 m
c)power=(p1-P2)q
=29.1*10³*6.082*10⁻³
Power =176.986 watt //watt is the unit of power
The difference in total pressure between two points on a network used to transport fluids is known as a pressure drop. When frictional forces acting on a fluid as it flows through the tube, brought on by the resistance to flow, occur, a pressure drop happens.
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Raw materials used of silicone rubber
Answers
The steel framework is used to support the reinforced stone concrete slab that is used for an office. The slab is 200 mm thick. Calculate the value of the distributed load on BE. Take a = 2 m, b = 5 m. Assume density for concrete slab = 23.6 kN/m3. Hint: Look at Example 2 from class notes.
Answers
Answer:
Total distributed load on BE = 5 m²
Explanation:
The first process is to get the value for the Dead load (DL) on the slab;
This is determined by using the formula:
DL = ρ × t
DL = 23.6 kK/m³ × 0.2 m
DL = 4.72 kN/m²
From table 1.4 which relates to the office buildings, we derive the value for the minimum live load (LL) = 2.40 kN/m³
Hence the total load TL = Dead Load DL) + Live loaf (LL)
DL = (4.72 + 2.40) kN/m³
DL = 7.12 kN/m³
Now; from the imaginative view of the information given; the member BE which get the load from half area of the panel BEDC & half the area of BEFA panel parallel to member BE; then the tributary area on member BE can be calculated as;
\(A_{BE} = ( \dfrac{a}{2}+\dfrac{a}{2}) \times width\)
\(A_{BE} = ( \dfrac{2}{2}+\dfrac{2}{2}) \times 1\)
\(A_{BE} =2\times 1\)
\(A_{BE} =2 m^2/m\)
The total distributed load acting on BE is:
\(Total \ load = TL \times A_{BE}\)
\(Total \ load = 7.12 \ \dfrac{kN}{m^2 }\times (2 \times \dfrac{m^2}{m})\)
Total load = 2.5 × 2
Total load = 5 m²
Do Problem 1.8 using Galerkin’s method instead of the potential energy approach. The strong form is
E\frac{\mathrm{d^2u} }{\mathrm{d} x^2} + \rho g = 0
????(0) = 0
????(????) = 0
Use a quadratic polynomial for approximating the function.
Use the minimum potential energy method and the Rayleigh-Ritz method to find the displacement and stress of the midpoint of the rod shown in Fig. P1.8. Compare results using both a quadratic and cubic polynomial for the Ritz approximation. x = 0 Body force per unit volume, pg - 1 E=1 A=1 hr-2 Figure P1.8
Answers
The weighted residual approach is another name for the Galerkin method. This strategy can be used to irregular geometry with a regular node layout.
If a differential equation's solution function is substituted, the differential equation will not be satisfied, and a residue will result. A continuous operator problem, such as a differential equation, which is frequently expressed in a weak formulation, can be transformed into a discrete problem in mathematics using the Galerkin methods, which are named after the Russian mathematician Boris Galerkin. This is done by applying linear constraints determined by finite sets of basis. In Galerkin's technique, the basis function that was used to generate the weighting function, Wi, is selected. arbitrary with the exception that must adhere to the homogenous border criteria.
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In unguided medium (free space), the electromagnetic (EM) signal wave spreads as it leaves the transmit antenna. Since the power of the EM signal resides at the surface area of the wave front, signal power is described as signal power density (i.e., watts per area).
a. True
b. False
Answers
Answer:
a. True
Explanation:
What is your creative solution for clean, sustainable, and accessible energy?
Answers
A soil sample collected in a 10-ha field had a wet weight of 412g. The sample was dried at 105°C to a constant weight of 308g. The apparent specific gravity and density of the soil particles are 1.2 and 2.5 g/cm³ respectively. Determine: (i) Water content on a volume bases [4] (ii) Water content as a depth in mm [2] (iii) Moisture deficit if the field capacity of the soil is 35% by weight [4]
Answers
Water content on a volume basis Water content on a volume basis (VWB) can be determined by the formula given below: First, we will find the weight of water and volume of soil.
The weight of water is determined by subtracting the weight of dry soil from the weight of wet soil.Weight of water = Weight of wet soil - Weight of dry soil= 412 g - 308 g = 104 gDensity of soil = 2.5 g/cm³Apparent specific gravity of soil particles = 1.2Density of water = 1 g/cm³Volume of soil = Weight of dry soil / Density of soil particles= 308 g / (1.2 × 2.5 g/cm³)= 102.7 cm³
Therefore, the water content on a volume basis is 101.2%.(ii) Water content as depth in mmWater content as depth in mm (D) can be determined by the formula given below:$\text{D}=\frac{\text{Weight of water}}{\text{Volume of soil}} \times \text{Depth of soil}$$We have already calculated the weight of water, volume of soil and the water content on a volume basis. We need to calculate the depth of soil first. Since the sample was collected in a 10-ha field, we will assume that the sample was collected at a depth of 15 cm.
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in a typical structural steel floor or roofing framing, there are three types of elements, called primary, secondary, and tertiary elements. explain what these are and what materials they consist of.
Answers
The primary components span along one the the path of the grid and guide the secondary elements that span the other grid path. The secondary components guide the tertiary factors, which span perpendicular to the secondary factors.
primary: beams or beamlike members
secondary: beams or beamlike members
tertiary: deck panels
A structural floor may be defined because of the real, structural part of your floor. That is a part of the floor that without a doubt preserves the ground up. Another type of floor might be taken into consideration as the end ground, and the end floor might really be the floor end. Primary factors - This represents essential factors like walls (outside and internal), floors (floor and upper floors), roofs, and stairs connecting the floors. There are interconnected structural elements. Secondary factors - These are the elements that replicate and whole the spaces.
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Compute the area and circumference of a circle given the radius r if the radius is greater than or equal to 1.0; otherwise, you should compute only the circumference. Repeat the algorithm as much as the user wants.
Answers
In this question we shall present the algorithm in pseudocode, whose structure is now summarized:
1) Inputs.
2) Algorithms.
3) Outputs.
Please notice that While-cycles consider the requirement of using the algorithm as many times as user wants.
Name: Area-or-Circunference
CHAR - decide
REAL - radius, circumference, area
Say "Do you want to calculate? [Y] - Yes/[N] - No";
Write decide;
While (decide != 'Y' and decide != 'y' and decide != 'N' and decide != 'n'):
Say "Invalid option. Do you want to calculate? [Y] - Yes/[N] - No";
Write decide;
end-While
While (decide = 'Y' or decide = 'y'):
Say "Please indicate a radius";
While (radius < 0):
Say "Radius must be equal or greater than 0. Please indicate a
radius";
Write radius;
end-While
If (radius < 1):
circumference = 2*3.14*radius;
Say "The circumference has a value of %circumference length units";
Else:
circumference = 2*3.14*radius;
area = 3.14*radius*radius;
Say "The circumference has a value of %circumference length units
and the area has a value of %area square units";
end-If
Say "Do you want to calculate? [Y] - Yes/[N] - No";
Write decide;
While (decide != 'Y' and decide != 'y' and decide != 'N' and decide !=
'n'):
Say "Invalid option. Do you want to calculate? [Y] - Yes/[N] - No";
Write decide;
end-While
end-While
If (decide = 'N' or decide = 'n'):
Say "Good luck";
end-If
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How does the Center of Gravity of a Robot Relate to the Translational, Rotational, or Oscillatory Motion Associated with it?
Answers
The center of gravity, also known as the balance point or point of rotation when an object is permitted to freely rotate, is the average location of an object's weight.
Explain about the Gravity?All objects with mass are attracted to one another by the gravitational attraction, which has a magnitude that is directly proportional to the masses of the two objects and inversely proportional to the square of their distance from one another.
By means of gravity, a planet or other body pulls items toward its core. All the planets are maintained in their orbits around the sun by the force of gravity.
Any particle of matter in the universe will gravitate toward any other with a force that varies directly as the product of the masses and inversely as the square of the distance between them, according to Newton's law of gravity.
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often, the conclusion of a set of instructions will contain maintenance tips and ______________.
Answers
Answer:
troubleshooting guidelines
Explanation:
Maintenance tips provide guidance on how to keep the system or item in good working condition, including regular cleaning, lubrication, or preventive measures to avoid common issues. They help ensure the longevity and optimal performance of the product.
Troubleshooting guidelines, on the other hand, provide assistance in identifying and resolving problems or issues that may arise during the usage of the system or item. They typically include step-by-step instructions or a list of common problems with corresponding solutions, enabling users to troubleshoot and fix issues independently.
Both maintenance tips and troubleshooting guidelines are essential components of instructions as they empower users to effectively maintain and address any potential issues with the system or item they are working with.
do not stop on railroad tracks or within __________ feet of the crossing.
Answers
Answer:
i think there are track pants or underwear ahh sorry wrong message
According to federal law, it is illegal to stop your vehicle on railroad tracks. In addition, drivers are required to stop at least 15 feet away from the nearest rail of a railroad crossing if a signal device is not present or is malfunctioning.
If there is a signal device present and it indicates that a train is approaching, drivers must stop their vehicles at a safe distance from the crossing. The reason for this law is to prevent accidents and ensure the safety of drivers and passengers in vehicles, as well as pedestrians and train passengers. Therefore, it is important to always be aware of railroad crossings and to follow the rules of the road when approaching them.
You should not stop on railroad tracks or within 15 feet of the crossing. It is crucial to maintain a safe distance from the tracks to prevent accidents involving trains and vehicles. Remember to always follow traffic signals and laws at railroad crossings to ensure safety for everyone.
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A liquid of specific heat 3000J/kgk rise from 15°c to 65°c in 1 min when an electric heater is used. If the heater generate 63000J, calculate the mass of the water
Answers
Answer:
0.42 kg
Explanation:
Heat is proportional to mass by way of the conversion factor that is the inverse of the specific heat.
\(\dfrac{63000\text{ J}}{\dfrac{3000\text{ J}}{\text{kg$\cdot$K}}\cdot(65-15)\text{ K}}=0.42\text{ kg}\)
The mass of the liquid is about 0.42 kg.
Languages such as COBOL, when used in a database environment, are called___.
data dictionaries.
clients.
retrieval/update facilities.
host languages.
data definition languages.
Answers
Languages such as COBOL, when used in a database environment, are called host languages.
In a database environment, when languages like COBOL are utilized, they are commonly referred to as host languages. Here is a detailed explanation of the options provided:
1. Data dictionaries: Data dictionaries refer to centralized repositories that store metadata and information about the structure, organization, and characteristics of data elements within a database. They are not specific to any programming language.
2. Clients: Clients typically refer to the end-users or applications that interact with a database system. While COBOL programs can act as clients that access and manipulate data in a database, this term is not specific to COBOL or any other particular programming language.
3. Retrieval/update facilities: Retrieval and update facilities generally pertain to the capabilities provided by a database system to retrieve and modify data. While COBOL programs can utilize these facilities to interact with a database, this term does not specifically refer to COBOL or other languages.
4. Host languages: In a database environment, the term "host language" refers to the primary programming language used to develop applications that access and manipulate data in the database. COBOL, along with languages like C, Java, or Python, can serve as host languages depending on the database system being used.
5. Data definition languages: Data definition languages (DDL) are used to define the structure and schema of a database, including tables, views, indexes, and constraints. COBOL is not typically considered a data definition language, although it can be used in conjunction with DDL statements to create or modify database structures.
Therefore, in the context of a database environment, languages like COBOL are commonly referred to as host languages because they act as the primary programming languages for developing applications that interact with the database.
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What is the importance of food handling machines in food industry (Explain in points).
Answers
Answer:
Explanation:
Profile photo for Rosie Milojevic
Rosie Milojevic, Business Development at iComplied
Answered 3 years ago
For those who run or work in a business that handles food, you understand the importance of food safety and regulation compliance as it pertains to not only to certification and licensing of a company, but also the life or death of those who consume the products. Because food safety is such an important issue, we want to ensure that all companies who work in the production, preparation, or processing of food have the tools and information they need to ensure they are in full compliance 100% of the time. One slip in food safety compliance could cost someone their health or life, and this information spreads mistrust in the general public toward the company who sold the product, and also the entire product across companies throughout an entire country and beyond. So how does each company working with food ensure they comply with each and every food safety regulation? Through excellent auditing tools.
Auditing in Food Safety Must Change
Auditing in food safety compliance is essential in ensuring that all regulations are being complied with. Most auditing practices for major companies are severely out of date. Many rely on several different forms, stacks of paperwork, and data stored on multiple different computers and databases. This is incredibly inefficient, as it can be easy to miss something when comparing one sheet to the next, and paper can easily be lost or destroyed. It is also time consuming for companies to share audits over separate computers and databases, as it must be passed down from one employee to the next. Technology has granted all food safety compliance managers a simple solution. Auditing apps are the new wave solutions for companies who want all of their data stored on one cloud database that is instantly accessible with real-time data for all employees. This means that no one ever gets left out of the loop, and no new information will fall through the cracks.
Iwant Solution for the question
Answers
The equations of function f(t) from the function f(s) are
\(f\left(t\right)=\frac{2}{t^2}-\frac{2}{t^2}e^{-t}-\frac{2}{t^2}e^{-4t}+\frac{2}{t^2}e^{-6t}\ +\frac{2}{t^2}e^{-7t}-\frac{2}{t^2}e^{-9t}\)
\(f\left(t\right)=\frac{1}{t^2}-\frac{1}{t^2}e^{-t}+\frac{2}{t^2}e^{-3t}-\frac{2}{t^2}e^{-4t}\ -\frac{1}{t^2}e^{-4t}-\frac{1}{t^2}e^{-5t}\)
\(f\left(t\right)=\frac{2}{t}-\frac{2}{t}e^{-t}-\frac{2}{t}e^{-3t}+\frac{4}{t}e^{-5t}\ -\frac{2}{t}e^{-7t}\)
Calculating the function f(t) from the function f(s)The function definitions are given as: f(s)
The relationship between s and t are not given
So, we assume that
s = t
This means that we substitute s = t in the functions f(s) and then evaluate the expression for f(t) in terms of t.
Using the above, we can not calculate the functions and then plot the graphs
The graphs are added as an attachment
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An interest rate of norminal 12% per year , compounded weekly is
Answers
Answer: It is a nominal rate per year
By now, you most likely already noticed there are many similarities between the technological design process and the scientific method. Using your own words, explain 3 ways in which these processes are similar. (This will be graded).
Answers
Answer:
The key to bieng a good engineer
1. Define Your Goals
2. Commit Yourself To Continuous Professional Development
3. Work On Improving Soft Skills
4. Understand Business
5. Embrace Change
6. Work Hard
7. Be Optimistic
8. Identify Role Models And Mentors
9. Stay Flexible
10. Focus On The Long-Term
Look at this website for more info.
https://slcontrols.com/us/10-tips-becoming-successful-engineer/
; How do engineers make a difference in the world and with proof ?
Answers
what is the transfer function? what is the steady-state error, ess? what is the natural frequency? you can assume ra
Answers
The transfer function is a mathematical representation of the relationship between the input and the output of a system. The steady-state error, or ess, is the difference between the desired output and the actual output when the system reaches a steady state. The natural frequency is the frequency of the system's response without any external forces.
Transfer Function: Transfer Function is used in signal processing, control engineering, and other disciplines that deal with systems or signals. The ratio of output to input in Laplace transform is known as the transfer function.
Steady-State Error: The error that happens when the system is at a stable state is referred to as a steady-state error. The difference between the desired and actual response is known as steady-state error. A system's ability to track a specific input as time progresses is characterized by this kind of error. If the input signal is a unit step, then the steady-state error is referred to as the static error coefficient. The coefficient of the steady-state error is frequently used to classify systems in control engineering.
Natural Frequency: Natural frequency is a term used in physics to describe how quickly an object vibrates when it is set in motion. The number of oscillations made by a system in a given time period without any external force acting on it is referred to as its natural frequency. A natural frequency is a measure of a system's stiffness and mass. In a control system, it is the frequency at which the system oscillates in the absence of any input.
A natural frequency is also known as an undamped natural frequency or a resonance frequency, and it is represented by the symbol \(\omega_n\).You can assume the following in the problem. If you have any specific values, kindly provide them.
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the city of raleigh has 10100 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 221 said they'd vote for brown, 357 said they'd vote for feliz, and 22 were undecided.
a. What is the population of this survey?
b. What is the size of the population?
c. What is the size of the sample?
d. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.
e. Based on this sample, we might expect how many of the 9500 voters to vote for Brown?
Answers
a. The population of this survey is the registered voters in the city of Raleigh, North Carolina.
b. The size of the population is 10100 registered voters.
c. The size of the sample is 600 registered voters who were surveyed.
d. The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 221/600 = 0.37.
e. Based on this sample, we might expect 37% of the 10100 voters to vote for Brown, which would be approximately 3700 voters.
A sample is a portion of a population that is selected for study or analysis. In this case, a sample of 600 registered voters in the city of Raleigh was selected to participate in a telephone poll to gauge their voting preferences for the upcoming city council election.
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is calculated by dividing the number of voters who said they'd vote for Brown (221) by the sample size (600). This gives us 0.37, or 37%.
However, it's important to note that the estimate of 3700 voters is just that - an estimate. There is always some level of uncertainty or error when making predictions based on a sample, as the sample may not be representative of the entire population. For example, the sample might have a different distribution of ages, races, or other demographic factors than the population as a whole.
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Which physical quantity measures the rate at which an object’s velocity changes?
A.
force
B.
speed
C.
acceleration
D.
torque
Answers
Acceleration is change is velocity over time. Rate is another word for time
Answer:
I think the answer is b speed
Explanation:
Technician A says that the body is bolted to the frame in a body-over-frame vehicle.
Answers
C) Both A and B. Hence Technician A says that the body is bolted to the frame in a body-over-frame vehicle is correct and Technician B says that a body-over-frame vehicle usually has the body welded to the frame kis correct.
What is the Technician about?Technician A is correct in saying that a body-over-frame vehicle may have front upper rails. Front upper rails are a type of structural member that can be used to reinforce the front of the vehicle's body-on-frame structure.
Technician B is also correct in saying that a body-over-frame vehicle usually has the body welded to the frame. In a body-over-frame design, the body of the vehicle is mounted onto a separate frame, and the two are joined together using bolts or welding.
Therefore, both technicians are correct in their statements.
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See full question below
Technician A says that a body-over-frame vehicle may have front upper rails.
Technician B says that a body-over-frame vehicle usually has the body welded to the frame.
Who is right?
A)
A only
B)
B only
C)
Both A and B
D) Neither A nor B
2. A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit
of surface area is twice as great for the for the hemisphere as it is for the cylindrical side wall. Determine the dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction.
Answers
An extremum is a point where the function has its highest or lowest value, and at which the slope is zero.
The dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum is as follows;
Height of cylinder = 2 × Radius of cylinderReason:
The given parameters are;
Form of silo = Cylinder surmounted by a hemisphere
Cost of construction of hemisphere per square unit = 2 × The cost of of construction of the cylindrical side wall
Required:
The dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum
Solution:
The fixed volume of the silo, V, can be expressed as follows;
\(V = \pi \cdot r^2 \cdot h + \dfrac{2}{3} \cdot \pi \cdot r^3\)
\(h = \dfrac{V - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 }\)Where;
h = The height of the cylinder
r = The radius of the cylinder
The surface area is, Surface Area = 2·π·r·h + 2·π·r²
The cost, C = 2·π·r·h + 2×2·π·r² = 2·π·r·h + 4·π·r²
Therefore;
\(C = 2 \times \pi \times r\times \dfrac{V - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 } + 4 \cdot \pi \cdot r^2 = \dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r}\)
\(C = \dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r}\)At the minimum value, we have;
\(\dfrac{dC}{dr} =0 = \dfrac{d}{dr} \left(\dfrac{8 \cdot r^3 \cdot \pi + 6 \cdot V}{3 \cdot r} \right) = \dfrac{16 \cdot r^3 \cdot \pi - 6 \cdot V}{3 \cdot r^2}\)Which gives;
16·π·r³ = 6·V
\(V = \dfrac{16 \cdot \pi \cdot r^3}{6} = \dfrac{8 \cdot \pi \cdot r^3}{3}\)Which gives;
\(h = \dfrac{\dfrac{8 \cdot \pi \cdot r^3}{3} - \dfrac{2}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 } = 2 \cdot r\)
h = 2·r
The height of the silo, h = 2 × The radius, 2
Therefore, the dimensions to be used if the volume is fixed and the cost is to be kept to a minimum is, height, h = 2 times the radius
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A drawing requires a welder to make a 1/4"" fillet weld 16"" long. What is the volume of weld metal required to make this weld?
Answers
Making sure that the length of the weld is also given in centimetres, multiply the length of the weld by the area to determine the volume.
How much welding metal is needed to make this weld?Making sure that the length is also given in centimetres, multiply the weld's length by its area to determine the volume. In this example, the volume is 507 cubic centimetres per metre (cu. cm/m), which is how volume is typically expressed.
Add the weld strength and size together. Subtract the above product from the maximum permitted tensile stress. To determine how long the weld joint is, multiply the result by 0.707.
By multiplying the parcel's length, width, and height (all expressed in centimetres) and dividing the result by 5000, volumetric weight is most frequently calculated (some carriers use a divisor of 4000).
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Calculate the percentage increase of the highest-paid bachelor’s-degree engineer in 2016 compared to the lowest-paid bachelor’s-degree engineer in 2016.
Answers
Explanation:
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