Problem #3. The "divide and average" method, an old-time method for approximating the square root of any positive number a can be formulated as x = x+a/x 2 Write a well-structured pseudocode to implement this algorithm as depicted in figure below. Use proper indentation so that the structure is clear. F SquareRoot = 0 a>0 F T tol = 10-5 x = a/2 y = (x + a/x)/2 e = |(y-x)/yl x=y e

Problem #3. The "divide and average" method, an old-time method for approximating the square root of any positive number a can be formulated as x = x+a/x 2 Write a well-structured pseudocode to implement this algorithm as depicted in figure below. Use proper indentation so that the structure is clear. F SquareRoot = 0 a>0 F T tol = 10-5 x = a/2 y = (x + a/x)/2 e = |(y-x)/yl x=y e

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 6PE

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(Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.
(Computation) Among other applications, Pascal’s triangle (see Figure 7.22) provides a means of determining the number of possible combinations of n things taken r at a time. For example, the number of possible combinations of five people (n = 5) taken two at a time (r=2)is10. Each row of the triangle begins and ends with 1. Every other element in a row is the sum of the element directly above it with the element to the left of the one above it. That is, element[n][r]=element[n1][r]+element[n1][r1] Using this information, write and test a C++ program to create the first 11 rows of a twodimensional array representing Pascal’s triangle. For any given value of n less than 11 and r less than or equal to n, the program should display the correct element. Use your program to determine in how many ways a committee of 8 can be selected from a group of 10 people
(Data processing) Your professor has asked you to write a C++ program that determines grades at the end of the semester. For each student, identified by an integer number between 1 and 60, four exam grades must be kept, and two final grade averages must be computed. The first grade average is simply the average of all four grades. The second grade average is computed by weighting the four grades as follows: The first grade gets a weight of 0.2, the second grade gets a weight of 0.3, the third grade gets a weight of 0.3, and the fourth grade gets a weight of 0.2. That is, the final grade is computed as follows: 0.2grade1+0.3grade2+0.3grade3+0.2grade4 Using this information, construct a 60-by-7 two-dimensional array, in which the first column is used for the student number, the next four columns for the grades, and the last two columns for the computed final grades. The program’s output should be a display of the data in the completed array. For testing purposes, the professor has provided the following data:
(Electrical eng.) a. An engineer has constructed a two-dimensional array of real numbers with three rows and five columns. This array currently contains test voltages of an amplifier. Write a C++ program that interactively inputs 15 array values, and then determines the total number of voltages in these ranges: less than 60, greater than or equal to 60 and less than 70, greater than or equal to 70 and less than 80, greater than or equal to 80 and less than 90, and greater than or equal to 90. b. Entering 15 voltages each time the program written for Exercise 7a runs is cumbersome. What method could be used for initializing the array during the testing phase? c. How might the program you wrote for Exercise 7a be modified to include the case of no voltage being present? That is, what voltage could be used to indicate an invalid voltage, and how would your program have to be modified to exclude counting such a voltage?
(Conversion) a. Write a C++ program to convert meters to feet. The program should request the starting meter value, the number of conversions to be made, and the increment between metric values. The display should have appropriate headings and list the meters and the corresponding feet value. If the number of iterations is greater than 10, have your program substitute a default increment of 10. Use the relationship that 1 meter = 3.281 feet. b. Run the program written in Exercise 6a on a computer. Verify that your program begins at the correct starting meter value and contains the exact number of conversions specified in your input data. c. Modify the program written in Exercise 6a to request the starting meter value, the ending meter value, and the increment. Instead of the condition checking for a fixed count, the condition checks for the ending meter value. If the number of iterations is greater than 20, have your program substitute a default increment of (ending value - starting value) / 19.
(Civil eng.) Write a C++ program to calculate and display the maximum bending moment, M, of a beam that’s supported on both ends (see Figure 3.8). The formula is M=XW(LX)/L, where X is the distance from the end of the beam that a weight, W, is placed, and L is the beam’s length. You program should produce this display: The maximum bending moment is xxxx.xxxx The xxxx.xxxx denotes placing the calculated value in a field wide enough for four places to the right and left of the decimal point. For your program, assign the values1.2,1.3,and11.2toX,W,andL.
(Statistical) In many statistical analysis programs, data values considerably outside the range of the majority of values are simply dropped from consideration. Using this information, write a C++ program that accepts up to 10 floating-point values from a user and determines and displays the average and standard deviation of the input values. All values more than four standard deviations away from the computed average are to be displayed and dropped from any further calculation, and a new average and standard deviation should be computed and displayed.
The program in the Programming Example: Fibonacci Number does not check whether the first number entered by the user is less than or equal to the second number and whether both the numbers are non-negative. Also, the program does not check whether the user entered a valid value for the position of the desired number in the Fibonacci sequence. Rewrite that program so that it checks for these things.
Mark the following statements as true or false. A double type is an example of a simple data type. (1) A one-dimensional array is an example of a structured data type. (1) The size of an array is determined at compile time. (1,6) Given the declaration: int list[10]; the statement: list[5] - list[3] * list[2]; updates the content of the fifth component of the array list. (2) If an array index goes out of bounds, the program always terminates in an error. (3) The only aggregate operations allowable on int arrays are the increment and decrement operations. (5) Arrays can be passed as parameters to a function either by value or by reference. (6) A function can return a value of type array. (6) In C++, some aggregate operations are allowed for strings. (11,12,13) The declaration: char name [16] = "John K. Miller"; declares name to be an array of 15 characters because the string "John K. Miller" has only 14 characters. (11) The declaration: char str = "Sunny Day"; declares str to be a string of an unspecified length. (11) As parameters, two-dimensional arrays are passed either by value or by reference. (15,16)
When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)
(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.
Redo Programming Exercise 8 using dowhile loops.