You must first divide the area into several smaller shapes, the centroids of which are easier to determine, in order to find the centroid of the shaded area indicated in Prob. F9-1.
This can be done by drawing lines to divide the area into triangles and rectangles, as shown in the figure below:
[asy] /* Made by MRENTHUSIASM */ size(8cm); draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); draw((1,0)--(1.5,0.5)--(1,1)); draw((0,0)--(0.5,0.5)--(0,1)); draw((0.5,0.5)--(1.5,0.5),dashed); draw((0.75,0)--(0.75,0.5),dashed); draw((0,0.5)--(1,0.5),dashed); label("$x$",(0.75,0),S); label("$y$",(0,0.5),W); [/asy]
Once the area has been divided, you can use the following formulas to determine the centroid of each smaller shape:
For a triangle:
$x = \frac{x_1 + x_2 + x_3}{3}$
$y = \frac{y_1 + y_2 + y_3}{3}$
where $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ are the coordinates of the three vertices of the triangle.
For a rectangle:
$x = \frac{x_1 + x_2}{2}$
$y = \frac{y_1 + y_2}{2}$
where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of two opposing vertices of the rectangle.
Once you have determined the centroids of all the smaller shapes, you can then use the following formula to determine the centroid of the entire shaded area:
$x = \frac{\sum_i A_i x_i}{\sum_i A_i}$
$y = \frac{\sum_i A_i y_i}{\sum_i A_i}$
where $A_i$ is the area of the $i$th smaller shape and $(x_i,y_i)$ is the centroid of the $i$th smaller shape.
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There are several books placed in the HackerStudy library. One of those books on mathematics described an interesting problem that a mathematician wishes to solve. For an array arrofnintegers, the mathematician can perform the following move on the array: 1. Choose an indexi(0≤i
Using the knowledge of computational language in python it is possible to write a code that There are several books placed in the HackerStudy library.
Writting the code:include<iostream>
using namespace std;
long getMaximumScore(int arr[],int k,int n)
{
long count=0,sum=0;
for(int i=0;i<n-1;i++)
{
for(int j=0;j<n-i-1;j++)
{
if(arr[j+1]>arr[j])
{
arr[j+1]=arr[j+1]+arr[j];
arr[j]=arr[j+1]-arr[j];
arr[j+1]=arr[j+1]-arr[j];
}
}
}
for(int i=0;i<n;i++)
{
if(count==k)
return sum;
else
{
sum=sum+arr[i];
count++;
}
}
}
int main()
{
int n,k;
cin>>n;
int arr[n];
for(k=0;k<n;k++)
cin>>arr[k] ;
cin>>k;
cout<<getMaximumScore(arr,k,n);
return 0;
}
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Explain what the engineering team should advise in the following scenario.
Situation: An engineering team is analyzing a problem with a dam near a large metropolitan area. The dam reservoir has a capacity of 300 billion cubic feet, and it produces hydroelectric power for local municipalities. The dam has developed a severe crack.
Answer: its c
Explanation:
To read signs you need good focal vision
Answer:eyesight
Explanation:
Electronic rack-and-pinion systems use an electric motor to pump the hydraulic fluid through the hoses.
a. true
b. false
Electronic rack-and-pinion systems use an electric motor to pump the hydraulic fluid through the hoses. This statement is true.
The rack and pinion gearset is housed inside a metal tube, with each end of the rack protruding out and being attached to an axial rod. This is how it operates. When the steering wheel is twisted, the rack is moved by the pinion gear, which is mounted to the steering shaft. Based on the torque being given to the steering wheel by the driver, the steering wheel position, and the vehicle's speed, the EPS electronic control unit (ECU) determines the amount of aiding power required. With an applied force, the EPS motor rotates a steering gear, lowering the driver's necessary torque.
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which of the following code segments will move the robot from the center square along the same path as the code segment above?
count ← 0
REPEAT 4 TIMES
{
count count + 1
REPEAT count TIMES
{
MOVE_FOWARD ()
}
ROTATE_LEFT ()
}
Which of the following best describes the typical method by which messages are transmitted over the Internet?The message is broken into bundles that are communicated in a predefined request. Every bundle should be gotten in the request it was sent for the message to be accurately reassembled by the beneficiary's gadget.
Which of the following best shows how keylogging can be used to get into a computer system without permission?A user installs a program on their computer that records and transmits all user input unintentionally.
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For the circuit shown below if Vp=26 V and resistor R dissipates 345.6 KJ
in 24 h. Find E1 and R.
The values obtained for R and E1 after solving the given circuit will be equal to 1 ohm and 38 V.
What is Electrical energy?Charged material experiences a force when exposed to an electromagnetic field because of the fundamental characteristic of electric charge. It's conceivable for electrical ions to be positive or negative. Two charges that are opposed to one another repel one another.
As per the given data in the question,
Vp= 26V and,
E₂ = 24V
V₂ = 26-24
= 2V
Given, R will lose 345.6KJ of energy in a day.
We must determine the energy wasted by R in 1 second in order to determine the power dissipated across R.
So,
PR = (345.6x103)J / (24x3600)sec
= 4 Watts
Also,
PR = I₂ x R
4 = I₂R (1)
V₂ = Voltage across R = 2V
2 = I x R
I = 2/R (2)
Substitute equation (2) in equation (1) we get
4 = 4/R
R = 1 ohm.
I = 2 ampere
Six ohms of resistance will not block the same current. So,
V₁ = 2X6
= 12 Volts
So,
Now, Apply KVL in the circuit,
E₁ = V₁ + Vp
= 12 + 26
E₁ = 38 V
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The pendulum consists of two slender rods AB and OC which have a mass of 3 kg / m. The thin plate has a mass of 12 kg / m2. Determine the location y- of the center of mass G of the pendulum, then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G.
The moment of inertia of the pendulum about an axis perpendicular to the page and passing through G will be 1.5 kgm².
A pendulum is a weight suspended from a pivot so that it can swing freely. The motion of a pendulum is a type of simple harmonic motion, which means that the pendulum moves back and forth in a regular, periodic fashion. The moment of inertia of an object is a measure of the object's resistance to change in its rotational motion.
To determine the location of the center of mass of the pendulum, we need to find the mass of each part and the distance from the center of mass of each part to point G.
The mass of rod AB is 3 kg/m * 1 m = 3 kg
The mass of rod OC is also 3 kg/m * 1 m = 3 kg
The mass of the plate is 12 kg/m2 * 1 = 12 kg
The distance from the center of mass of rod AB to point G is 0.5 m (since the rod is 1 m long and point G is at the midpoint of the rod)
The distance from the center of mass of rod OC to point G is also 0.5 m
The distance from the center of mass of the plate to point G is 0.5 m (since the plate is 1 m wide and point G is at the midpoint of the plate)
Now we can use the formula for the location of the center of mass:
yG = (3 kg * 0.5 m + 3 kg * 0.5 m + 12 kg * 0.5 m) / (3 kg + 3 kg + 12 kg) = 0.5 m
To calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G, we can use the formula for the moment of inertia of a rod about its center of mass:
[tex]I = (1/12) * m * L^2[/tex]
For rod AB:
[tex]I = (1/12) * 3 kg * (1 m)^2 = 0.25 kg*m^2\\[/tex]
For rod OC:
[tex]I = (1/12) * 3 kg * (1 m)^2 = 0.25 kg*m^2[/tex]
For the plate:
I = (1/12) * 12 kg * (1 m)^2 = 1 kg*m²
The total moment of inertia of the pendulum is the sum of the moments of inertia of the individual parts:
I = 0.25 kgm^2 + 0.25 kgm^2 + 1 kgm^2 = 1.5 kgm²
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a standard penetration test (spt) was performed at a depth of 10 ft in sand of unit weight 120 lb/ft 3 . the n-value was found to be 26. determine the corrected n-value by the two methods presented in this chapter
Using the principle of substitution, the value of the expression given is 162.
Find the solution ?The sampler has an outer diameter of 51 mm and is driven into the soil using a 63.5 kg weight that has a 760 mm free fall.One ignores the top 150 mm of soil.The test is the following 300 mm of soil.
Given the expression :
6x⁴y³
x = -1 ; y = 3
Substituting the values into the expression :
6(-1)⁴(3)³
-1⁴ = - 1 × - 1 × - 1 × - 1 = 1
3³ = 3 × 3 × 3 = 27
6(1)(27) = 6 × 1 × 27 = 162
Hence, the value of the expression is 162.
Using the principle of substitution, the value of the expression given is 162.
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During a pregame warmup period, two basketballs collide above the hoop when in the positions shown. Just before impact, ball 1 has a velocityv 1 which makes a 26 ∘ angle with the horizontal. If the velocityv 2 of ball 2 just before impact has the same magnitude as v 1 determine the two possible values of the angle θ(θ 1<θ 2) measured from the horizontal, which will cause ball 1 to go directly through the center of the basket. The coefficient of restitution ise=0.74
Measure of Restitution When the velocity vectors of two objects are parallel, direct collisions between them happen. While energy is lost during the impact when one or both of the objects are bent.
What is the coefficient of restitution's mathematical equation?v 2−v 1=−e(u 2−u 1). This equation represents Newton's law of restitution. The restitution coefficient always meets the condition 0e1. The balls stay in contact with one another after a collision when e=0.
What makes coefficient of restitution crucial?It is crucial to understand the coefficient of restitution since it establishes whether a collision is elastic or inelastic in nature. Whether a collision is elastic or not reveals whether there is any kind of kinetic energy loss as a result of the impact.
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3. (10 pts) Let T be a MST of a given graph G. Will T still be the MST if we reduce the weight of exactly one of the edges in G by a constant c? Prove your answer Solution
Explanation suggests that the MST will not be the same as T when it converts to T.
What is a minimum spanning tree (MST)?A minimum spanning tree (MST) for a weighted, connected and undirected graph is a spanning tree with weight less than or equal to the weight of every other spanning tree.
The new weight will be smaller than the original weight, or wnew < wnew, if we precisely lower the weight of one edge (let's say e).
There may now be two cases. - The modified edge e is a part of T and is a member of the MST. Since e is already a component of T, reducing its weight will also reduce the MST's weight. Consequently, the modified MST T is the same as the present MST T. (but with reduced weight by c).
The modified edge e does not belong to the MST since it is not a component of T. This might alter the existing MST since another MST that includes the updated edge e might exist with a lower weight. The MST does not change, thus if we find a situation where this is not the case, our assumption would be erroneous and T would not be the MST. This may be demonstrated by contradiction.
We may use the cyclic property of MST, which states that in order to obtain an MST, we need to eliminate the edge with the biggest weight in the cycle. The red edge in this graph was not included in the MST, hence its weight was reduced. The MST and the red edge combine to create a graph with a cycle. Using the cyclic property, subtract the cycle C's strongest edge to obtain the adjusted MST. O(V) time (where |V| is the number of vertices) can be used to complete this.
This suggests that the MST will not be the same as T when it converts to T.
Therefore, T will not surely be the MST if we reduce the weight of exactly one of the edges in G by a constant c as described by point 2.
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Which of these is shown in the animation below?
A. Air spring
B. Coil spring
C. Shock absorber
D. Torsion bar
solved there are many ways to generate the sum of squares of all integers until a given upper bound. one of these ways is to use the producer-consumer paradigm. declare fun {generate n limit} if n
The producer-consumer paradigm is a type of programming technique that involves two separate processes which communicate with one another in order to achieve a desired result.
What is producer-consumer paradigm?
The producer-consumer paradigm is a computer programming model in which producers create and store data in a shared buffer, while consumers retrieve and use the data. The paradigm is based on the idea that producers and consumers are separate entities and that each has its own thread of execution. This separation allows for the asynchronous transfer of data between producers and consumers. The producer-consumer paradigm is used in many applications, including operating systems, databases, and distributed computing. In the producer-consumer paradigm, the producer thread produces data and places it in a shared buffer. The consumer thread then retrieves the data from the buffer and uses it. In order to ensure that the producer and consumer threads do not interfere with each other, the producer must wait until the consumer has finished using the data before producing more. This is done by using synchronization mechanisms such as semaphores, monitors, and message queues.
The producer creates items (in this case, a list of the squares of all integers until a given upper bound), and the consumer processes them (in this case, by summing them together).
To use this paradigm to generate the sum of squares of all integers until a given upper bound, we need to define two functions: the producer and the consumer.
The producer will take two inputs: n, the current number being processed, and limit, the upper bound. The production function should check if n is at or below the limit, and if so, it should create a list containing the square of n. If n is greater than the limit, it should return an empty list.
The consumer will take in a single input, which should be the list created by the producer. The consumer should iterate through the list and sum up the values inside. It should then return the sum.
Once those functions have been defined, we can create a loop which calls the producer to generate lists until it reaches the upper bound, and then passes those lists to the consumer for processing. Once the loop is complete, the consumer will have returned the sum of squares of all integers until the given upper bound.
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What are the steps to configure your router in order?
Answer:
Explanation:Step 1: Decide where to place the router. ...
Step 2: Connect to the Internet. ...
Step 3: Configure the wireless router gateway. ...
Step 4: Connect gateway to router. ...
Step 5: Use app or web dashboard. ...
Step 6: Create a username and password. ...
Step 7: Update the router's firmware. ...
Step 8: Create a Wi-Fi password.
Which of the following types of auditing requires access to source code? Question options: Use Case Testing Code Review In order for a subject to be _____, the system must first ____ the subject and then record the subject's actions. Question options: accountable, identify accountable, authorize A company needs to conduct testing of technical controls as part of an IT Security Audit. Which of the following types of testing allows the auditor to have full knowledge of the internals for the system(s) under test at the time the tests are being designed or selected? Question options: White box testing Gray box testing What is the primary difference between second party and third party audits? Question options: Second party audit teams are granted inside access to the organization's operations. Third party audit teams are limited in their access to the organization's operations. Second party audits are external audits conducted on behalf of a business partner. Third party audits are conducted to provide assurance of compliance with laws and regulations. Red Team testing has revealed weaknesses in how a company provisions and deprovisions user accounts. These weaknesses allowed the Red Team to exploit the username/login for a privileged account assigned to a system administrator who recently left the IT department for another position within the company. Which of the following is the most important business process to investigate to learn why the weaknesses exist so that they can be addressed using a policy-based solution? Question options: User Account Review Privileged identity management
Code reviews, often known as peer reviews, serve to ensure the quality of the code base. Code reviews are rigorous analyses of code that are intended to detect flaws, improve code quality, and assist engineers in learning the source code.
To hold a subject accountable, the system must first approve the subject before recording the subject's behavior.
"White box testing" allows the auditor to have complete knowledge of the internals of the system(s) under test at the time the tests are devised or selected.
Because audit results may affect the customer's purchasing decisions, second-party audits are more formal than first-party audits. A third-party audit is carried out by an audit agency that is independent of the customer-supplier relationship.
User Account Review is the most critical business process to analyze in order to determine why the gaps exist and how they may be remedied utilizing a policy-based solution.
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Suppose a student table has two columns, names and marks. How to get name and marks of top three students
Answer:
SELECT Name, Marks FROM Student s1 where 3 <= (SELECT COUNT(*) FROM Students s2 WHERE s1.marks = s2.marks)
1. A business would use a website analytics tool for all of the following EXCEPT _____.
A. viewing the number of pages a person visited
B. viewing the number of new and returning visitors
C. viewing why someone visited your webpage
D. deciding when to increase bandwidth
2. After creating a webpage with HTML code, what do you need to do so that others can access it on the Internet?
A. Specify the format
B. Publish to a web server
C. Convert to a read-only file
D. Compress pages and multimedia content
3. An Integrated Development Environment (IDE) stores files and folders for your website in a directory called _____.
A. a project
B. an FTP client
C. an absolute reference
D. a consortium
4. Anita is developing a website for her photography business. On the home page, she wants to include a link to another webpage in her website. What type of link should she insert?
A. absolute reference
B. relative reference
C. targeted reference
D. blank reference
Answer:
1. C
2. B
3. A
4. B
Explanation:
A business would use a website analytics tool for all of the following EXCEPT _____.
C: viewing why someone visited your webpage
After creating a webpage with HTML code, what do you need to do so that others can access it on the Internet?
B: Publish to a web server
An Integrated Development Environment (IDE) stores files and folders for your website in a directory called _____.
A: a project
Anita is developing a website for her photography business. On the home page, she wants to include a link to another webpage in her website. What type of link should she insert?
B: relative reference
on linux, flex is the fast lexical analyzer generator. the file scanner.lex contains the description of tokens to generate a simple and very basic scanner using flex. to generate the scanner, use the following command: flex scanner.lex you should notice that flex created the file lex.yy.c in your current directory. now compile this file into
To compile the lex.yy.c file generated by flex, you can use the command: gcc lex.yy.c -o scanner.
This command will compile the lex.yy.c file and generate a scanner executable file.
What is compile?
Compiling is the process of taking source code written in a programming language, such as Java, and converting it into a format that can be read and executed by a computer. The compiled code is usually referred to as an executable, which is a file that contains a set of instructions that can be run by a computer. Compiling source code is a crucial step in the development of any software program or application. Compiling source code allows developers to create efficient and reliable programs that are optimized for specific hardware and operating systems. Additionally, compiling source code allows for faster execution of the program, since the computer does not need to interpret the source code each time the program is run. Furthermore, compiling source code can make it easier to debug and improve the code, since errors are easier to catch in the compiled form.
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identify the conclusions that can be drawn from the given premises using existential generalization. (check all that apply.)Check All That Apply a. There exists a non-six-legged creature that eats a six-legged creature. b. There does not exist a non-six-legged creature that eats a six-legged creature. c. There exists a noninsect that eats an insect d. There does not exist a noninsect that eats an insect.
A non-six-legged animal that eats a six-legged animal does not exist. Using existential generalization, it is possible to infer from the stated premises that there is a non-insect that eats an insect.
Existential generalization rule: what is it?A valid method of inference in predicate logic that enables one to proceed from a specific statement, or one instance, to a quantified generalized statement, or existential proposition, is known as existential generalization (also known as existential introduction, or I).
What purpose does existential and universal instantiation serve?When something is true of everything, it must also be true of the specific thing that the constant c names. This is known as universal instantiation. When making existential generalizations, it is important to remember that if anything is true of if c is a specific constant, then it applies to at least something.
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All of the following sequences are stages of the machine cycle EXCEPT _________.
fetch
decode
sort
store
Only these people are allowed to attend Sprint Retrospective a. Scrum master and Development team b. Product owner and Development team c. Scrum master and Product owner d. Scrum Team
It is to be noted that only these people are allowed to attend Sprint Retrospective are: "Scrum master and Development team" (Option A)
What is the Sprint Retrospective?The Sprint Retrospective is a meeting that takes place at the conclusion of each sprint in Scrum. It allows the Scrum team to reflect on the previous sprint and identify methods to enhance the process in the future.
It's aim is to identify what went well during the sprint, what may be improved, and how to achieve those improvements in the future. It is an essential component of the Scrum framework since it ensures that the team is always developing and changing to meet the demands of the project.
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Structural engineers use wireless sensor networks to monitor the condition of dams and bridges.
a. True
b. False
Answer: True
Explanation:
Structural engineering is simply referred to as a branch of civil engineering, and they help in the designing of structures like buildings, dams, tunnels, bridges, tunnels, etc. Structural engineers typically work as consultants.
Wireless sensor networks are used by structural engineers to monitor the condition of dams and bridges. Wireless sensor network refers are dedicated sensors that are used in monitoring the physical conditions of the bridges and to know if they're still in good conditions.
Which of the following situations best describes the chemical weathering process of sedimentary rock?
answer choices
Sedimentary sandstone is carried away by water along the bedrock of a stream.
Sedimentary sandstone allows water to freeze and thaw inside its cracks.
Sedimentary limestone cliffs are battered by strong ocean waves.
Sedimentary limestone is exposed to acid rain at the top of a mountain.
A situation which best describes the chemical weathering process of sedimentary rock include the following: D. Sedimentary limestone is exposed to acid rain at the top of a mountain.
What is weathering?In Geology, weathering can be defined as a biogeochemical process that involves both the physical and chemical breakdown of rock into smaller pieces or fragments called sediments.
Additionally, weathering is broadly classified into two (2) categories and these include the following;
Physical weatheringChemical weatheringDuring the chemical weathering process of sedimentary rock, sedimentary limestone that are found at the top of a mountain become exposed to acid rain.
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6.5 Determine the vorticity field for the following velocity vector: V=(x^2-y^2)i -2xyj
The vorticity field for the following vector in the question is 0.
The step by step explanation of the calculation is given in the figure attached below. The term "vorticity" refers to a pseudovector field that depicts the tendency for anything to rotate or the local spinning motion of a continuum near a point as observed by an observer standing at that location and moving with the flow. It is a significant quantity in the dynamical theory of fluids and offers a useful foundation for comprehending a number of intricate flow phenomena, such as the development and motion of vortex rings. The vorticity, for instance, is two times the angular velocity vector of the rotation in the central core of a Rankine vortex, which is a mass of continuum revolving like a rigid body. If there is shear, the vorticity could still be non-zero even if all particles are moving in a straight, parallel line.
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In a parking garage, each level is 18 feet apart, Each ramp to a level is 120 feet long. Find the measurement of elevation for each ramp?
Answer:
Sin(angle)=0.1538
Angle=arcsine(0.1538)
Angle is 8.85 degrees
Explanation:
Firstly draw a diagram showing a triangle with the required angle, a hypotenuse of 130 ft and an opposite side of 20 ft.
The sine of the angle required uses the formula Opposite/Hypotenuse
(i am not sure sure)
What kind of data is captured in a data warehouse?
A data warehouse is created specifically for data analytics, which includes scanning vast amounts of data to recognize patterns and relationships.
A database is used to collect and store data, including transactional information. Enterprise Data Warehouse (EDWH) is another name for Data Warehouse (DWH) (EDW). A data warehouse is a central location where information from one or more data sources is stored. Enterprise Data Warehouse (EDW), Operational Data Store (ODS), and Data Mart are the three primary types of data warehouses. A data warehouse acts as a repository for old information that may be analyzed. Data in a warehouse can be examined and evaluated using online analytical processing, or OLAP.
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Which of these parts reduces the amount of pollutants in the engine exhaust?
A. Transmission
B. Catalytic converter
C. Tailpipe
D. Muffler
Answer:
Option B
Explanation:
Catalytic convertor with in the exhaust pipes of any vehicle converts harmful gases (such as hydrocarbons (HC), carbon monoxide (CO) and nitrogen oxides (NOx)) produced by combustion of fossil fuels (petrol, diesel etc.) into less harmful/toxic pollutants by acting as a catalyst for redox reaction. A catalytic convertor releases some mild gases from the exhaust like less harmful CO2, nitrogen and water vapour (steam)
Hence, option B is correct
list all the variables, along with the program unit where they are declared, that are visible in the bodies of sub1, sub2, and sub3. assuming static scoping is used.
Here is the list of all variables, along with the program unit where they are declared, that are visible in the bodies of sub1, sub2, and sub3:
sub1: a(sub1), y(sub1), z(sub1), x(main)sub2: a(sub2), b(sub2), z(sub2), y(sub1), x(main) (y(sub1)sub3: a(sub3), x(sub3), w(sub3), y(main), z(main)What is variables?Information that needs to be accessed and changed by a computer programme is stored in variables. In order to make our programmes more understandable to ourselves and the reader, they also offer a way to label data with a descriptive name.
To understand variables better, think of them as data storage units. Labeling and archiving data in memory is their only function. When used throughout your programme, this data will be useful.
One of the most challenging aspects of computer programming is naming variables. Be very careful when choosing names for your variables. Make every effort to name your variable something that is both accurate and clear to another reader.
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Three spheres are subjected to a hydraulic stress. The pressure on spheres 1 and 2 is the same, and they are made of the same material. The fractional compression on the third sphere is equal to the fractional compression on the first sphere times the reciprocal of the fractional compression on the second. If the pressure on the third sphere is 150000 N/m2 , what is the Bulk Modulus for the third sphere
Answer:
"150000 N/m²" is the right approach.
Explanation:
According to the question, the pressure on the two spheres 1 and 2 is same.
Sphere 1 and 2:
Then,
⇒ [tex]P_1=P_2[/tex]
⇒ [tex]\frac{\Delta V_1}{V_1}=\frac{\Delta V_2}{V_2}[/tex]
and the bulk modulus be,
⇒ [tex]B_1=B_2[/tex]
Sphere 3:
⇒ [tex]\frac{\Delta V_3}{V_3} =\frac{\frac{\Delta V_1}{V_1} }{\frac{\Delta V_2}{V_2} } =1[/tex]
then,
⇒ [tex]P_3=B\times \frac{\Delta V_3}{V_3}[/tex]
⇒ [tex]=B\times 1[/tex]
⇒ [tex]=150000\times 1[/tex]
⇒ [tex]=150000 \ N/m^2[/tex]
Air flows through a pipe at a rate of 200 L/s. The pipe consists of two sections of diameters 20 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, if the inlet temperature of air is at 25oC, due to the compression of the air at neck of the pipe contraction, the outlet temperature is measured at 30oC, determine the differential height of water between the two pipe sections. Take the air density at 25oC and 35oC as 1.20 kg/m3 and 1.19 kg/m3 respectively.
Answer:
To determine the differential height of water between the two sections of the pipe, we need to consider the conservation of energy and the ideal gas law.Conservation of energy:
The first law of thermodynamics states that the increase in internal energy of a system is equal to the heat added to the system, minus the work done by the system. In this case, the internal energy of the air flowing through the pipe increases as it is compressed in the neck of the pipe, causing its temperature to increase.The increase in internal energy can be expressed as:ΔU = Q - Wwhere ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.Ideal gas law:
The ideal gas law states that the pressure of an ideal gas is directly proportional to its temperature and inversely proportional to its volume. This can be expressed as:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature.Solution:
To determine the differential height of water between the two sections of the pipe, we need to use the conservation of energy and the ideal gas law to relate the pressure difference between the two sections to the temperature difference and the flow rate of the air.First, let's convert the flow rate of the air from liters per second to cubic meters per second:200 L/s = 0.2 m3/sNext, we can use the ideal gas law to express the pressure difference between the two sections in terms of the temperature difference and the flow rate:ΔP = (nRT1 - nRT2)/V = (1.20 kg/m3 * 8.31 J/(molK) * 298 K - 1.19 kg/m3 * 8.31 J/(molK) * 303 K)/(0.2 m3/s)ΔP = -27.7 PaFinally, we can use the conservation of energy to express the differential height of water in terms of the pressure difference and the flow rate:Δh = ΔP/ρg = (-27.7 Pa)/(1000 kg/m3 * 9.81 m/s2) = -0.28 mTherefore, the differential height of water between the two sections of the pipe is -0.28 m.Note that the negative sign indicates that the pressure is lower in the second section of the pipe, which is consistent with the fact that the temperature is higher and the volume is lower in this section.
Explanation:
Fill in the blank to output the quotient of dividing 100 by 42. print (100______42)
Answer:
print(100/42)
Explanation:
This is the operand for division in python and some other languages.