Hello, could you help me? Read a program We consider the following algorithm in which n denotes a natural number. r <— n As long as r > equal to 5 r <— r -5 End while 1. What value does r take at the end of the algorithm? rhythm if we give n the value 8? 2. Quote two integers which give at the end of the algorithm the same r value. 3. What does the r value obtained at the end of the algorithm represent compared to n? Thanks in advance!
1. Given that r initial value is set to n, and the algorithm continuously subtracts 5 from r as long as r is greater than or equal to 5, the value of r at the end of the algorithm would be 3. This is because once r becomes less than 5, the algorithm will stop subtracting 5 from it.
2. Two integers that would give the same final value of r are 8 and 13. If n is initially 8, then r would be 3 at the end of the algorithm. Similarly, if n is initially 13, r would also be 3 at the end.
3. The value of r obtained at the end of the algorithm represents the remainder when n is divided by 5. In other words, it represents the difference between n and the largest multiple of 5 that is less than or equal to n.
Sure! Let's go through each question step by step.
1. What value does r take at the end of the algorithm if we give n the value 8?
We start with r = n, so r = 8 initially. Then, in each iteration of the while loop, we subtract 5 from r as long as r is greater than or equal to 5. So, the algorithm will iterate once, and we will have r = 8 - 5 = 3 at the end.
2. Quote two integers which give the same r value at the end of the algorithm.
To find two integers that give the same r value at the end, we would need to find two different values of n that result in the same final value of r. Let's go through a few examples:
Example 1:
If n = 8, then the final value of r is 3.
If n = 18, then the final value of r is also 3.
Example 2:
If n = 11, then the final value of r is 1.
If n = 21, then the final value of r is also 1.
So, in the first example, both n = 8 and n = 18 give the same final value of r = 3. And in the second example, both n = 11 and n = 21 give the same final value of r = 1.
3. What does the final value of r obtained at the end of the algorithm represent compared to n?
The final value of r represents the remainder when n is repeatedly divided by 5. It gives us the "leftover" value after subtracting multiples of 5 from n. In other words, if we have n as the starting point, the algorithm calculates r as the remainder when we repeatedly subtract 5 from n until it becomes less than 5. So, the final value of r can also be thought of as the modulo operation (n % 5).
I hope this helps! Let me know if you have any further questions.
Certainly! Let's analyze the algorithm step by step to answer your questions:
1. What value does r take at the end of the algorithm if we give n the value 8?
To answer this question, we need to run the algorithm with n = 8 and track the value of r. Starting with r = n = 8, we enter the while loop. Since 8 is equal to or greater than 5, we subtract 5 from r, making it 3. We continue iterating because r is still greater than or equal to 5. Next, we subtract 5 from r again, making it -2. However, we exit the loop because -2 is no longer greater than or equal to 5. Therefore, the final value of r is -2.
2. Quote two integers which give the same r value at the end of the algorithm:
In order to find two integers that give the same r value, we need to consider values of n that result in the same final r. Let's choose two examples:
Example 1: n = 18
Following the algorithm, we subtract 5 from r until it becomes less than 5:
- n = 18, r = 18
- r = r - 5 = 13
- r = r - 5 = 8
- r = r - 5 = 3
- r = r - 5 = -2
Example 2: n = 23
Again, following the algorithm:
- n = 23, r = 23
- r = r - 5 = 18
- r = r - 5 = 13
- r = r - 5 = 8
- r = r - 5 = 3
- r = r - 5 = -2
Both examples yield the same final value of r, which is -2. Therefore, the integers 18 and 23 give the same r value at the end of the algorithm.
3. What does the r value obtained at the end of the algorithm represent compared to n?
The r value obtained at the end of the algorithm represents the remainder of the division of n by 5. It tells us how much is left after repeatedly subtracting 5 from n until it is less than 5. In mathematical terms, r = n % 5, where % is the modulo operation.