1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Damm [24]
3 years ago
12

How many different messages can be transmitted in n microseconds using three different signals if one signal requires 1 microsec

ond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
Computers and Technology
1 answer:
SIZIF [17.4K]3 years ago
6 0

Answer:

a_{n} = 2/3 . 2^n + 1/3 . (-1)^n

Explanation:

Let a_{n} represents number of the message that can transmitted in <em>n </em>microsecond using three of different signals.

One signal requires one microsecond for transmittal: a_{n}-1

Another signal requires two microseconds for transmittal: a_{n}-2

The last signal requires two microseconds for transmittal: a_{n}-2

a_{n}= a_{n-1} + a_{n-2} + a_{n-2} = a_{n-1} + 2a_{n-2}, n ≥  2

In 0 microseconds. exactly 1 message can be sent: the empty message.

a_{0}= 1

In 1 microsecond. exactly 1 message can be sent (using the one signal of one  microseconds:

a_{0}= 1

2- Roots Characteristic equation

Let a_{n} = r^2, a_{n-1}=r and a_{n-2}= 1

r^2 = r+2

r^2 - r - 2 =0                 Subtract r+6 from each side

(r - 2)(n+1)=0                  Factorize

r - 2 = 0 or r +1 = 0       Zero product property

r = 2 or r = -1                 Solve each equation

Solution recurrence relation

The solution of the recurrence relation is then of the form a_{1} = a_{1 r^n 1} + a_{2 r^n 2} with r_{1} and r_{2} the roots of the characteristic equation.

a_{n} =a_{1} . 2^n + a_{2}.(-1)"

Initial conditions :

1 = a_{0} = a_{1} + a_{2}

1 = a_{1} = 2a_{1} - a_{2}

Add the previous two equations

2 = 3a_{1}

2/3 = a_{1}

Determine a_{2} from 1 = a_{1} + a_{2} and a_{1} = 2/3

a_{2} = 1 - a_{1} = 1 - 2 / 3 = 1/3

Thus, the solution of recursion relation is a_{n} = 2/3 . 2^n + 1/3 . (-1)^n

You might be interested in
Robert is leading a project online that includes students from different cultures. Two of the students spend most of the time li
enyata [817]

Answer:

A & C

Explanation:

8 0
3 years ago
What occurs in a steam engine?
VARVARA [1.3K]
Fist one correct.
second wrong because not all heat is used for work, some of it lost to other.
third wrong because fuel burn inside is called combustion engine
 <span />
7 0
3 years ago
Read 2 more answers
Pick the 3 correct Python functions that parse and output only the date and time part of each log in log.txt as follows.
Mila [183]

Answer:

1, 4, 5

Explanation:

parse2:

. In this case it's passing "r" as an argument, which really does absolutely nothing, because whenever you call open("file.txt") it defaults to reading mode, so all you're doing is explicitly passing the "r". So let's look at the first line. Whenever you call str.split() without any arguments, by default it splits it by empty text, and filters any empty text. So str.split() is not the same as str.split(" ") although it has similar behavior. "     ".split(" ") will output ['', '', '', '', '', ''], while "     ".split() will output []. So in this case the line.split() will split the string '10.1.2.1 - car [01/Mar/2022:13:05:05  +0900] "GET /python HTTP/1.0" 200 2222' into the list<em> ['10.1.2.1', '-', 'car', '[01/Mar/2022:13:05:05', '+0900]', '"GET', '/python', 'HTTP/1.0"', '200', '2222'].</em> As you can see the the data is split into two pieces of text, AND they include the brackets in both strings. So when it gets the 3 index and strips it of the "[]" it will have the incomplete date

parse3:

 In this instance the "r" does nothing as mentioned before the "r" is already defaulted whenever you call open("file.txt") so open("file.txt") is the same as open("file.txt", "r"). So in this case we won't be working left to right, we're going inside the brackets first, kind of like in math you don't don't work left to right in equation 3 + 3(2+3). You work in the brackets first (inside brackets you do left to right). So the first piece of code to run is the line.split("[" or "]"). I actually kind of misspoke here. Technically the "[" or "]" runs first because this doesn't do what you may think it does. The or will only return one value. this is not splitting the line by both "[" and "]". The, or will evaluate which is true from left to right, and if it is true, it returns that. Since strings are evaluated on their length to determine if they're true. the "[" will evaluate to true, because any string that is not empty is true, if a string is empty it's false. So the "[" will evaluate to true this the "[" or "]" will evaluate to "[". So after that the code will run line.split("[") which makes the list: <em>['10.1.2.1 - car ', '01/Mar/2022:13:05:05  +0900] "GET /python HTTP/1.0" 200 2222']</em>. Now the [3:5] will splice the list so that it returns a list with the elements at index 3 (including 3) to 5 (excluding 5). This returns the list: [], because the previous list only has 2 elements. There are no elements at index 3 to 5 (excluding 5). So when you join the list by " ", you'll get an empty string

parse4:

  So I'm actually a bit confused here, I thought the "r+" would open the file in read-writing mode, but maybe this is a different version of python I have no idea, so I'm going to assume it is reading/writing mode, which just means you can read and write to the file. Anyways when you split the line by doing line.split(), as mentioned before it will split by empty spaces and filter any empty spaces. This line will return: <em>['10.1.2.1', '-', 'car', '[01/Mar/2022:13:05:05', '+0900]', '"GET', '/python', 'HTTP/1.0"', '200', '2222']</em>. and then you splice the list from indexes 3 to 5 (excluding 5). This will return the list: <em>['[01/Mar/2022:13:05:05', '+0900]']</em> which has the two pieces of information you need for the date. Now it joins them by a space which will output: '[01/Mar/2022:13:05:05 +0900]'. Now when you strip the "[]" you get the string: '01/Mar/2022:13:05:05 +0900' which is the correct output!

parse 5:

 So in this example it's using re.split. And the re.split is splitting by "[" or "]" which is what re.split can be used for, to split by multiple strings, which may be confused by string.split("[" or "]") which is not the same thing as explained above what the latter does. Also the reason there is a backslash in front of the [ and ] is to escape it, because normally those two characters would be used to define a set, but by using a \ in front of it, you're essentially telling regex to interpret it literally. So in splitting the string by "[" and "]" you'll get the list: <em>['10.1.2.1 - car ', '01/Mar/2022:13:05:05  +0900', ' "GET /python HTTP/1.0" 200 2222']</em> which has 3 elements, since it was split by the [ and the ]. The second element has the date, so all you need to do is index the list using the index 1, which is exactly what the code does

8 0
1 year ago
Please!! I need help, this is due by tonight!!!
lyudmila [28]

Answer:

sorry if it is too late but I think it is d

Explanation:

4 0
3 years ago
In the microsoft powerpoint wiew ribbon. Which presentation wiew enables a user to view one slide at a time in the slide pain?
german

Answer:

The answer to this question is given below in the explanation section.

Explanation:

In the Microsoft PowerPoint view ribbon. A normal presentation view enables a user to view one slide at a time in the slide pain.

As we know that there are different views of presentation, such as, normal view, reading view, slider sorter, outline view, and note pages.

Only a Normal view allows you to see one slide at a time in the slide pain.

6 0
3 years ago
Other questions:
  • What is a way to minimize technical problems with computer
    13·1 answer
  • Whos ready for sao ordinal scale this march!!!( ಥـْـِـِـِـْಥ)
    7·1 answer
  • A model release can be either oral or written down. true or false
    11·2 answers
  • Sophie Black works as a computer programmer for a software company. Her boss, Mike Jones, is responsible for developing a new so
    8·1 answer
  • Write a statement that increases the value of the int variable total by the value of the int variable amount. that is, add the v
    5·1 answer
  • Your program will search for prime numbers. You will first ask the user for the range of values to search, and use for loops to
    6·1 answer
  • Three common risk factors for young drivers and how you plan to minimize these factors.
    13·1 answer
  • Which of the following would be better communicated with an image than with text?
    9·1 answer
  • The complete process for learning through repetition is to read, write, say, rest and revisit the information. Please select the
    12·2 answers
  • assuming the default gateway is connected to the internet, what type of internet access would this server have?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!