Which of the following algorithms has lowest worst case time complexity?a) Insertion sortb) Selection sortc) Quick sortd) Heap sort

Answers

Answer 1

Heap Sort and -Merge Sort both have runtime complexity that is O(nlogn), which is the best case scenario.

What are the complexity Mcq in the worst case?

The complexity of a bubble sort is O(n2) in the worst case and O in the best scenario (n). In a linear search strategy, the worst case scenario is when an item is either the very last entry in the array or not there at all.

What are the ideal and idealised temporal complexity scenarios?

In the best situation, linear search has an O time complexity (1). The temporal complexity is O in the worst case scenario (n).

To know more about complexity visit:-

https://brainly.com/question/20709229

#SPJ4


Related Questions

Refer to the film, actor, and film_actor tables of the Sakila database. The tables in this lab have the same columns and data types but fewer rows. Write a query that: Computes the average length of all films that each actor appears in. Rounds average length to the nearest minute and renames the result column "average". Displays last name, first name, and average, in that order, for each actor. Sorts the result in descending order by average, then ascending order by last name. The query should exclude films with no actors and actors that do not appear in films. Hint: Use the ROUND() and AVG() functions.

Answers

Using the knowledge of computational language in python it is possible to write a code that organizes film, actor and film and actor at the same time.

Writting the code:

SELECT a.last_name, a.first_name, ROUND(AVG(f.length)) AS 'average'

FROM film f

INNER JOIN film_actor fa ON f.film_id = fa.film_id

INNER JOIN actor a ON a.actor_id = fa.actor_id

GROUP BY a.last_name, a.first_name

ORDER BY average DESC, last_name ASC;

See more about python at brainly.com/question/18502436

#SPJ1

Design a class named Cake. Data fields include two string fields for cake flavor and icing flavor and numeric fields for diameter in inches and price. Include methods to get and set values for each of these fields. Create the class diagram and write the pseudocode that defines the class. Design an application that declares two Cake objects and sets and displays their values.

Answers

Using the computer language in pseudocode to write a function code that  declares two Cake objects and sets and displays their values.

Writting the code in pseudocode:

- cake flavor: string

- icing flavor: string

-diameter: num

-price: num

+set cake flavor (cake flavor : string) : void

+set icing flavor (icing flavor: string) : void

+set Diameter(size : num) : void

+set Price(price : num) : void

+get cake flavor () : string

+get cing flavor () : string

+get Diameter() : num

+get Price() : num

Answer A=

Pseudocode:

class Cake

Declarations

private string cake flavour

private string icing flavor

private num diameter

private num price

public void set Cake flavour (string Cake flavour)this. Cake flavour = Cake flavour

return

public void set icing flavour (string icing flavour)this. icing flavour = icing flavour

return

public void set Diameter(num size)

diameter = size

return

public void set Price(num price)

this price = price

return

public string get Cake flavour ()

return Cake flavour

public string get icing flavour ()

return icing flavour

public num get Diameter()

return diameter

public num get Price()

return price

end Class

start

Declarations

Cake my Cake

Cake your Cake

myCake.set cake flavour (“chocalate”)

myCake.set icing flavour (“peppermint”)

myCake.setDiameter(15)

myCake.setPrice(18)

myCake.set cake flavour (“pineapple”)

myCake.set icing flavour (“orange ”)

yourCake.setDiameter(20)

yourCake.setPrice(25)

output “Cake 1 info:”

output myCake.get cake flavour ()

output myCake.get icing flavour ()

output myCake.getDiameter()

output myCake.getPrice()

output Cake 2 info:”

output yourCake.get cake flavour ()

output yourCake.get icing flavour ()

output yourCake.getDiameter()

output yourCake.getPrice()stop

See more about pseudocode at brainly.com/question/13208346

#SPJ1

A company needing a network to connect its offices in montana, idaho, and utah would require a:_______

Answers

A company that needs a network to connect its offices in states such as Montana, Idaho, and Utah would require a: wide area network (WAN).

What is a WAN?

WAN is an abbreviation for wide area network and it can be defined as a type of telecommunication network that covers a wide range of geographical locations (regions) such as states, especially for the purpose of communication between different users that are residing in different countries or regions across the world.

In this context, we can infer and logically deduce that any company that needs a network to connect its offices and group of employees working in different states such as Montana, Idaho, and Utah would require a wide area network (WAN).

In conclusion, a wide area network (WAN) is a type of telecommunication network that is designed and developed to connect different states such as Montana, New York, Idaho, and Utah.

Read more on WAN here: brainly.com/question/8118353

#SPJ1

________ tells users how to use software and what to do if software problems occur.

Answers

Answer:

Documentation tells users how to use software and what to do if software problems occur.

Explanation:

Documents and Standard Operating Procedures (SOPs) help users use the software that they want to use. This is an advantage to whoever is selling the software so that they don't receive customer complaints and people continue to buy their product.

________ controls fix a trespass into the network. a. corrective b. detective c. preventive d. mitigating

Answers

Answer: Answer: corrective

Explanation:

What is an identifier that an online transaction is safe?

Answers

Answer: Look for third-party verification from TRUSTe or the Better Business Bureau symbol.

Explanation:

Having an SSL certificate is a sign that online transactions are secure. Secure Sockets Layer, or SSL, is a cryptographic technology that enables secure Internet communications.

A website's SSL certificate ensures that any data sent between the user's browser and the website's servers is encrypted and protected from unauthorized access. Look for the secure connection indicator "https://" at the beginning of the website's URL. Additionally, look for the padlock icon in the address bar to verify encryption. Some websites may show a green address bar or organization name if they have Extended Validation SSL certificates.

Learn more about SSL certificate, here:

https://brainly.com/question/32251706

#SPJ6

An instructor has given a student an assignment to assemble a pc. in which situation should the student be aware that esd is an issue?

Answers

When installing RAM situation is one where the student should be aware that esd is an issue.

What is the RAM in a computer?

RAM is a term that connote random-access memory and a computer RAM is known to be a kind of a short term memory and it is a place where data is said to be saved as at the time that the processor needs it.

Hence, When installing RAM scenario is one where the student should be aware that esd is an issue and then one can resolve it.

See full question below

An instructor has given a student an assignment to assemble a PC. In which situation should the student be aware that ESD is an issue?

when installing RAMwhen working in a corporate environment that has carpet installed under tower PCswhen using a grounded mat and working on a computer on an ungrounded workbenchwhen installing a dual-voltage power supply

Learn more about RAM from

https://brainly.com/question/13196228

#SPJ1

A photograph is created by what
A) Silver
B) Shutters
C) Light
4) Mirror

Answers

A photograph is created by Light.

What are photographs made of?

Any photograph created is one that is made up of Support and binders.

The steps that are needed in the creation of a photograph are:

First one need to expose or bring the film to light.Then develop or work on the imageLastly print the photograph.

Hence, for a person to create a photograph, light is needed and as such, A photograph is created by Light.

Learn more about photograph from

https://brainly.com/question/25821700

#SPJ1

As a member of the help desk administration team, you've been assigned to update the driver for the network adapter that is installed on most of the machines in your department. You have a copy of the latest driver on a USB flash drive. Which Windows utility will allow you to manually update this new driver?

Answers

The Windows utility that will allow you to manually update this new driver is called the Device Manager.

What is a Device Manager?

This is known to be a form of Computer program or a kind of a component of  a Microsoft Windows operating system that is said to give room for one to be able to see and control the hardware that is said to be attached to the computer.

Hence, The Windows utility that will allow you to manually update this new driver is called the Device Manager.

Learn more about Windows utility from

https://brainly.com/question/20659068

#SPJ1

What should you point out when demonstrating the confident cornering of a 2023 murano awd through a sweeping curve?.

Answers

The features to  point out when demonstrating the confident cornering of a 2023 Murano awd through a sweeping curve are:

How good the vehicle tracks as it goes into the curveHow level Murano is balanced.The strong grip of the tires.

What is the 2023 Nissan Murano about?

For 2023, the Murano is seen to be  having a lot of overdue makeover and it is one that includes a feature of improvement such as  revamp of the outside and interior.

Note that The features to  point out when demonstrating the confident cornering of a 2023 Murano awd through a sweeping curve are:

How good the vehicle tracks as it goes into the curveHow level Murano is balanced.The strong grip of the tires.

Learn more about Cars from

https://brainly.com/question/27950070

#SPJ1

Assign 20 to variables x, y and z in a single statement.

Answers

Answer:

x=y=z=20

Explanation:

This assigns the same value, which is 20 to multiple variables

The application that Scott is writing has a flaw that occurs when two operations are attempted at the same time, resulting in unexpected results when the two actions do not occur in the expected order. What type of flaw does the application have

Answers

The type of flaw that the application is said to  have is known to be called race condition.

What is meant by race condition?

A race condition is known to be a form of unwanted situation that takes place when a device or system tries to carry out two or more operations at the same given time, but due to the nature of the device or system, the operations had to b be done in the right sequence to be carried out correctly.

Therefore, The type of flaw that the application is said to  have is known to be called race condition.

Learn more about race condition from

https://brainly.com/question/13445523

#SPJ1

This flaw is called a race condition.

What is a race condition?

The term race condition in this context refers to an error that occurs when a program attempts to perform two operations simultaneously. In other words, when two operations are attempted at the same time, this leads to a failure in execution since the two operations do not occur in the expected order.

You can learn more about race condition here https://brainly.com/question/13445523

#SPJ1

Write a script named copyfile.py. this script should prompt the user for the names of two text files. the contents of the first file should be input and written to the second file.

Answers

Based on the above, The  script named copyfile.py.  is written in the image attached.

What is a script?

In regards to computer programming, a script is known to be a kind of a computer  program or we can say a sequence that is known to be made up of a lot of instructions that is often seen to be interpreted or done by another program instead of the computer processor.

Note that  some languages have been birth a lot expressly and they are known to be the script languages.

Therefore, scripting language or we say script language is known to be a programming language that is is often used to alter , customize, and automate what we say the facilities of any existing system.

Hence,  Based on the above, The  script named copyfile.py.  is written in the image attached.

Learn more about script  from

https://brainly.com/question/3700565

#SPJ1

Which of the following commands can be used to display socket information out to the terminal screen

Answers

Linus ss

Explanation:

The ss (socket statistics) command provides a lot of information by displaying details on socket activity. One way to get started, although this may be a bit overwhelming, is to use the ss -h (help) command to get a listing of the command's numerous options. Another is to try some of the more useful commands and get an idea what each of them can tell you.

One very useful command is the ss -s command. This command will show you some overall stats by transport type. In this output, we see stats for RAW, UDP, TCP, INET and FRAG sockets.

In the u. S. , what are the privacy rights that workers have with respect to emails sent or received in the workplace?

Answers

In the U. S. , what are the privacy rights that workers have with respect to emails sent or received in the workplace is that:

Workers have a little privacy protections in regards to workplace emails.

What is the above case about?

Email are known to be often used to send or transmit a one-way messages or be involved in two-way communication and as such;

In the U. S. , what are the privacy rights that workers have with respect to emails sent or received in the workplace is that:

Workers have a little privacy protections in regards to workplace emails.

Learn more about privacy rights from

https://brainly.com/question/2857392

#SPJ1

When is it permissible to access non va websites for personal use using va computers?

Answers

It is permissible only during one's break time or after a person is done with their duty hours and it is only for a short time and it is legal and also ethical.

What is a website?

This is known to be a form of is a composition of publicly accessible, interconnected Web pages that is known to often share a one domain name.

Based on the scenario above, It is permissible only during one's break time or after a person is done with their duty hours and it is only for a short time and it is legal and also ethical.

Learn more about websites from

https://brainly.com/question/13171394

#SPJ1

Given the IPv4 address in CIDR notation 215.200.110.50/25, identify the subnet ID that this address belongs to.

Answers

215.200.110.00, 215.100.110.64, 215.200.110.128,215.100.110.192

What operator must be overloaded if you want to use the standard library sort with a class such as Time

Answers

The operator that must be overloaded if you want to use the standard library sort with a class such as Time is <.

What is an Overload operator?

In computer programming, operator overloading, is known to be a kind of ad hoc polymorphism that entails different operators where they have different kinds of implementations based on their arguments.

Hence, The operator that must be overloaded if you want to use the standard library sort with a class such as Time is <.

See full question below

What operator must be overloaded if you want to use the standard library sort with a class such as Time?

A) ==

B) >

C) <

D) All of these

Learn  more about operator  from

https://brainly.com/question/13411600

#SPJ1

7.6 lab: replacement words write a program that finds word differences between two sentences. the input begins with the first sentence and the following input line is the second sentence. assume that the two sentences have the same number of words. the program displays word pairs that differ between the two sentences. one pair is displayed per line. ex: if the input is: smaller cars get better gas mileage tiny cars get great fuel economy then the output is: smaller tiny better great gas fuel mileage economy hint: store each input line into a list of strings.

Answers

The program that finds word differences between sentences (according to the description) above is given below.

What is a program?

A program is a set of codes and or instructions that are written sequentially and deliberately such that the computer, when it reads and executes them give a specific and premedicated output.

The lines of code that gives the output described above is:

import java.util.Scanner;  public class LabProgram {

     public static int findWordInWordList(String[] wordList, String wordToFind, int numInList) {

       for (int i = 0; i < numInList; i++) {

            if (wordList[i].equals(wordToFind)) {

                return i;

            }         }         return -1;

    }      public static void main(String[] args) {

        Scanner scnr = new Scanner(System.in);

         String[] original = new String[20], modified = new String[20];         int numInList = scnr.nextInt();

        for (int i = 0; i < numInList; i++) {

            original[i] = scnr.next();

           modified[i] = scnr.next();

        }          int numWords = scnr.nextInt();

        String[] words = new String[numWords];

        for (int i = 0; i < numWords; i++) {

            words[i] = scnr.next();

        }          int index;

       for (int i = 0; i < numWords; i++) {

           index = findWordInWordList(original, words[i], numInList);             if (index != -1)

                words[i] = modified[index];

        }          for (int i = 0; i < numWords; i++)             System.out.print(words[i] + " ");

        System.out.println();     } }

Learn more about programing:
https://brainly.com/question/23275071
#SPJ1

If we increase the sample rate of a device from 48khz to 96khz, what is the impact to the network?

Answers

If we increase the sample rate of a device  then A 96kHz subscription will need about  twice as much bandwidth as that of  48kHz subscription.

What is subscription?

The definition of a subscription is known to be a term that connote a form of an agreement that a person make in advance to get something for a given time period.

Hence, If we increase the sample rate of a device  then A 96kHz subscription will need about  twice as much bandwidth as that of  48kHz subscription.

Learn more about subscription from

https://brainly.com/question/15301858

#SPJ1

which of the following is acomputer program that detects, prevents. and takes action sto deactivate or remove malicious programmsd

Answers

Answer:

antivirus software is the answer to prevent computer from malicious program

The appropriate software to use for writing and editing research papers is ________ software.

Answers

The appropriate software to use for writing and editing research papers is word processing software.

What is a word processing software?

A word processor is a computer application that allows you to create and edit text documents on a computer. It is a multifunctional software for writing, with different typography (fonts/fonts), font sizes, colors, paragraph types, artistic effects and other options.

With a word processor, however, it is possible to delete and edit the content at any time, as its basic functionality is performed on the screen. Once the writing task has been completed, the user has the option of saving the document on a computer medium (either on the computer's hard disk, on the Internet or on a CD) or printing the material.

Several people make use of this software, such as students from schools and colleges, resarchers, professionals working in the field of Law, engineers, teachers, among other people who need a program to edit or create text files.

See more about computing at: brainly.com/question/13027206

#SPJ1

With the use of unshielded twisted-pair copper wire in a network. What causes crosstalk within the cable pairs?

Answers

The action that causes crosstalk within the cable pairs is the magnetic field around the adjacent pairs of wire.

What is crosstalk in communication?

Crosstalk is known to be a kind of a scenario or a phenomenon where the signal that are seen to be transferred on one channel of a mobile communication system forms a kind of an undesired effect on another channel.

Note that the poor frequency reuse in regards to the use of cellular networks is one that starts the co-channel interference and also one that leads to causes crosstalk.

Hence, The action that causes crosstalk within the cable pairs is the magnetic field around the adjacent pairs of wire.

Learn more about network from

https://brainly.com/question/1027666

#SPJ1

See full question below

With the use of unshielded twisted-pair copper wire in a network, what causes crosstalk within the cable pairs?

the magnetic field around the adjacent pairs of wire

the use of braided wire to shield the adjacent wire pairs

the reflection of the electrical wave back from the far end of the cable

the collision caused by two nodes trying to use the media simultaneously

PLEASE HELP!! And please don't just answer for points.

This question is from my animation class.

What was the “aha!” moment or breakthrough that Ulbrich describes?

Answers

Answer:

What was the aha moment or breakthrough that Ulbrich describes?

Explanation:

The “aha!” moment was when the found out about a new type of technology, called contour. This helped them create their character in a much better way.

Suppose your program frequently tests whether a student is in a soccer team, what is the best data structure to store the students in a soccer team?

Answers

The best data structure to store the students in a soccer team is the use of HashSet.

What is a Program?

This refers to the set of instructions that are given to a computer program in order to execute the instructions.

Hence, we can see that based on the fact that a computer program needs to frequently test whether a student is in a soccer team, the best data structure to store the students in a soccer team is a HashSet

Read more about computer programs here:

https://brainly.com/question/23275071

#SPJ1

A directory service is being installed on an exclusively windows network. which directory service software would be appropriate to install?

Answers

A directory service software that would be appropriate to install on an exclusively Windows network is an: Active Directory.

What is a directory service?

A directory service can be defined as a software system that's designed and developed to store, organize and provide end users with a name and an access to directory information, so as to effectively and efficiently unify (synchronize) all network resources.

In this scenario, an Active Directory is a directory service software that would be appropriate to install on an exclusively Windows network because it uses Lightweight Directory Access Protocol (LDAP).

Read more on directory services here: brainly.com/question/15187174

#SPJ1

The equals method of the Object class returns true only if the two objects being compared:_________
a) have identical attributes.
b) are the same object.
c) are aliases of each other.
d) are == to each other.
e) All of these are correct.

Answers

Answer:

Option b) are the same object.

Explanation:

The equals is used to compare the two objects based on the equality of the objects and if they share the same memory address. Thus the same objects will return the same memory address in which case method requires true.

== and equals method are different in terms of comparison, identical attributes may not lead to the output being true.

Sort the following everyday examples of sedimentary processes into the bins labeled with the sedimentary processes they most closely represent.

Answers

The Sorting of the  examples of sedimentary processes are:

Sediment Erosion/transport - The dirt going down the drain after you give your dog a bath and drain the tub Dirt being blown off a patioDeposition of sediment - Dust collecting on furnitureWeathering of rock - Tree roots extending into a rock layer and breaking it down Ice expanding in a crack in the road creating a potholeCompaction/lithification - A dump truck dumps a load of gravel on your lawn. The dirt below it becomes more consolidated

What is the sedimentary process known as?

Sedimentary rocks are said to be the outcome of

1) The weathering of preexisting rocks,

2) The transport of the weathering products,

3) The  deposition of the material.

4) The  compaction process.

5) The cementation of the sediment to form a rock.

This is known to be the most vital geological processes that has lead to the making of sedimentary rocks such as due to erosion, weathering, dissolution, and others

Therefore, The Sorting of the  examples of sedimentary processes are:

Sediment Erosion/transport - The dirt going down the drain after you give your dog a bath and drain the tub Dirt being blown off a patioDeposition of sediment - Dust collecting on furnitureWeathering of rock - Tree roots extending into a rock layer and breaking it down Ice expanding in a crack in the road creating a potholeCompaction/lithification - A dump truck dumps a load of gravel on your lawn. The dirt below it becomes more consolidated

See full question below

Sort the following everyday examples of sedimentary processes into the bins labeled with the sedimentary processes they most closely represent. Drag the appropriate items into their respective bins View Available Hint(s) Reset Heip A dump truck dumps a load of gravel on your lawn. The dirt below it becomes more consolidated Dirt being blown off a patio Ice expanding in a crack in the road Dust collecting on furniture creating a pothole Tree roots extending into a rock layer you give your dog The dirt going down the drain after a bath and drain the tub and breaking it down Sediment Erosion/transport Deposition of sediment Weathering of rock Compaction/lithification

Learn more about sedimentary processes from

https://brainly.com/question/13291293

#SPJ1

A(n) Blank______ database model stores data in the form of logically related two-dimensional tables. Multiple choice question. warehouse relational real-time

Answers

Answer:

relational database model

Explanation:

a. Mohit has bought a new laptop. The laptop is not working as no software is installed in
Which software should be installed first to make his laptop start working?​

Answers

The windows software should be installed first to make his laptop start working.

What is the Microsoft Windows?

This is known to be the Operating system and it is one that  is said to be made up  of a group of a lot of proprietary graphical operating system families made and marketed by Microsoft.

Note that the windows comes in different version such as:

Windows 11windows 10windows 8windows 7, etc.

Therefore, for your laptop to start, it need to have one of the windows written above.

The windows software should be installed first to make his laptop start working. and by installing the windows be it windows 10, 8, 7, etc., it will start working.

Learn more about software from

https://brainly.com/question/1538272

#SPJ1

Other Questions
what is the name of the "supercontinent" that once covered nearly one-third of the earth's surface recall that the halting problem is undecidable. show it is undecidable if a given turing machine ever returns to its initial state when started on a blank tape. which part of the sun's atmosphere has the lowest density (number of atoms per unit volume)? Use the compound interest formula to compute the total amount accumulated and the interest earned. $4000 for 3 years at 5% compounded quarterly The total amount accumulated after 3 years is $ __________ How grams of Ti metal will be deposited from a Tit4 solution by passing a current of 200 amps for 1 hour? modern industrial societies have the mere appearance of a teardrop. this is different the pyramidal structure of the past by the fact that: gyromagnetic ratios for 1h and 13c are 2.6752 x 108 t -1 s -1 and 6.7283 x 107 t -1 s -1 . find the resonant frequencies of these two nuclei at 3.0 t magnetic field. part a complete the atomic orbital (ao) and molecular orbital (mo) energy diagram for li2 . I need help with this math a. given a perfect bst with n = 255, what is the worst case (largest) number of comparisons?b. given a non-perfect bst with height = 6, what is the worst case (largest) number of comparisons? margaret died owning a passive investment in which her basis was $25,000. the fair market value of the asset included in her estate was $150,000, and she had $200,000 of suspended passive activity losses associated with the asset at the time of her death. which of the following is the amount of suspended losses that can be deducted on margaret's final tax return? a. $0. b. $25,000. c. $75,000. d. $200,000. Elja Associates performed an attest engagement to report on Brooktree Pharmaceuticals' Year 1 compliance with federal laws for quality assurance of a specific medication manufactured by the company. The engagement took place from December 15, Year 1, through February 10, Year 2, the date of the examination report. The practitioner found Brooktree Pharmaceuticals to be in compliance with the laws during Year 1. However, separately they became aware that the company was not in compliance with the laws during the first week of February, Year 2. Elja determined that this noncompliance was significant. Which section of the authoritative literature describes how Elja should report such noncompliance?Enter your response in the answer fields below. Guidance on correctly structuring your response appears above and below the answer fields. the data placement alternative in which a complete copy of the database is kept at each site is ___ data design is about modeling the architectural view of the system. group of answer choices true false find the taylor series for f centered at 6 if f (n)(6) = (1)nn! 5n(n 3) . what landform and/or vegetation pattern dominates in australia? deserts mountains plains forests wetlands a)The mathematical equation relating the independent variable to the expected value of the dependent variable that is,E(y) = 0 + 1x,is known as theregression model.regression equation.estimated regression equationcorrelation model. A new embankment, when completed will occupy a net volume of 257,000cy. The borrow material that will be used to construct this fill is stiff clay. In its "bank" condition, the borrow material has a moist unit weight of 129pcf, a water content of, 16.5% and an in place void ratio of 0.620. The embankment will be constructed in layers of 8 inch depth, loose measure then compacted to a dry unit weight of 114pcf at a moisture content of 18.3%. Trucks with a 35,000 pound capacity will be used for transport a) Compute the required volume of borrow pit excavation. b) Determine how many trucks will be required to complete the job. c) Determine how many gallons of water will need to be added to each truck. (1gallon of water is 8.36 pounds) evaluate the double integralImage for double integral ye^x dA, where D is triangular region with vertices (0, 0), (2, 4), and (0, 4)?ye^x dA, where D is triangular region with vertices (0, 0), (2, 4), and (0, 4)? definite Integrals2 - a) Set up but do not evaluate, Integral from (2)^(6) e^x sin x dx as the limit of a Riemann Sum. You can choose x_i^* as right endpoints of the interaval [x_i,x_(i+1)].2 - b) Set up and then use limits and the formula: sum_(i=1)^(n) i^2 = 1/6 n(n+1) to find the exact value of integral from (0)^(2) s x^2 dx. When discussing this problem please clearly express math.