Absolute C++
6th Edition
ISBN: 9780133970784
Author: Walter Savitch, Kenrick Mock
Publisher: Addison-Wesley
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Chapter 1, Problem 8PP
The Babylonian
- Make a guess at the answer (you can pick n/2 as your initial guess).
- Compute
- Set guess
- Go back to step 2 for as many iterations as necessary. The more steps 2 and 3 are repeated, the closer guess will become to the square root of n.
Write a
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The Babylonian algorithm to compute the square root of a positive number n is asfollows:1. Make a guess at the answer (you can pick n/2 as your initial guess).2. Compute r = n / guess3. Set guess = (guess +r)/ 24. Go back to step 2 for as many iterations as necessary. The more you repeat steps2 and 3, the closer guess will become to the square root of n.
Write a program that inputs a double for n, iterates through the Babylonian algo-rithm five times, and outputs the answer as a double to two decimal places. Your
answer will be most accurate for small values of n.
Eulers number e is used as the base of natural logarithm. It may be approximated using the formula
e=1/0!+1/1!+1/2!…1/(n-1)!+1/n!
When n is sufficiently large. Write a program that approximates e using a loop that terminates when the difference between the two successive values of e is less than 0.0000001.
The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner:
1. Compute the remainder of dividing the larger number by the smaller number.
2. Replace the larger number with the smaller number and the smaller number with the
remainder.
3. Repeat this process until the smaller number is zero.
The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their
GCD.
An example of the program input and output is shown below:
Enter the smaller number: 5
Enter the larger number: 15
The greatest common divisor is 5
Chapter 1 Solutions
Absolute C++
Ch. 1 - A metric ton is 35,273.92 ounces. Write a program...Ch. 1 - A government research lab has concluded that an...Ch. 1 - Workers at a particular company have won a 7.6 pay...Ch. 1 - Negotiating a consumer loan is not always...Ch. 1 - Write a program that determines whether a meeting...Ch. 1 - Prob. 6PPCh. 1 - One way to measure the amount of energy that is...Ch. 1 - The Babylonian algorithm to compute the square...Ch. 1 - The video game machines at your local arcade...Ch. 1 - Write a program that allows the user to enter a...
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