5. The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero.
procedure gcd(a, b)
if a b then gcd(a, b) := = gcd (b, a)
else if a = 0 then gcd (a, b) = b
else if a = 1 then gcd (a, b) :
:=1
else if a and b are even then gcd(a, b) 2gcd(a/2, b/2) := else if a is odd and b is even then gcd(a, b) := gcd(a, b/2)
else gcd(a, b) := gcd(a, b - a)
Use this algorithm to compute
(a) gcd(124, 244)
(b) gcd (4424, 2111).u
Answers
Implementating the given algorithm in python 3, the greatest common divisors of (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation is given below and the output of the sample run is attached.
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
#since it's a recursive function, it recalls the function with new parameters until a certain condition is satisfied
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
Learn more :https://brainly.com/question/25506437
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Step-by-step explanation:
This is a combination question: how many ways can you pick 2 people from a group of 10?
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Answers:
v = 54y = 0u = 6w = -48x = -1===================================================
Explanation:
The left hand side is
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}[/tex]
That -6 outside the matrix is multiplied with each item inside the matrix. This is known as scalar matrix multiplication. Effectively, it's very similar to the idea of the distributive property.
So for the first row, we have the three columns of: -6*3 = -18 and -6*(-1) = 6 and -6*3 = -18
The other two rows are handled the same way. This is what should result:
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]
From here, you'll then match up the terms in the given right hand side matrix. The top row has the variable 'u' in the middle, which matches with the '6' in the middle of the top row shown. Therefore, u = 6.
-----------------------------
Now to the second row.
The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.
Also, we have -6x in the middle which matches with the 6 in the same corresponding spot. Solving -6x = 6 leads to x = -1.
-----------------------------
Finally, the third row.
There's only one variable here and that's the variable y in the bottom right corner. It pairs up with 0 in the same corresponding spot for the right hand side matrix. Therefore, y = 0.
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Question 19
A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?
A. 52
B. 158
C. 210
D. 213
E. 218
Answers
Answer:
D. 213Step-by-step explanation:
The number of black pieces is 5 more than 3 times the white pieces:
b = 3w + 5Let the number of rounds is x.
Initial number of white nd black pieces:
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w = 7*7 + 3 = 52b = 3*52 + 5 = 161w + b = 52 + 161 = 213Correct choice is D
Answer:
A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?
A. 52
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D. 213
E. 218
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Answer:
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Step-by-step explanation:
100 divided by 5 plus 25 times 3 is 95 :)
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A
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B. The rate of change is the number of inches grown per month, and
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Step-by-step explanation:
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Step-by-step explanation:
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