Observe the following code for a function bisection: def bisection(f, a, b, N): for i in range(N): m = (a+b)/2 if f(a)*f(m)<0: b = m elif f(m)*f(b)<0: a = m return (a+b)/2 Below are five pieces of code, each of which calls this bisection function, and some of which depend on some variable y, that has already been assigned to some fixed integer. Match each piece of code with the value that it produces. bisection (lambda x: x**2-14*x+y, 7, 10, 100) (lambda y: bisection (lambda x: x**2-14*x+y, 7, 10, 100)) (47) bisection (lambda x: x**2-14*x+y, 7, 10, 5) bisection (lambda x: 5000*x-42071, 7, 10, 100) bisection (lambda x: x**2-14*x+y, 4, 7, 100) Choose... Choose... 8.732050807568877 8.734375 8.414213562373094 5.2679491924311215 8.414200000000001

Observe the following code for a function bisection: def bisection(f, a, b, N): for i in range(N): m = (a+b)/2 if f(a)f(m)<0: b = m elif f(m)f(b)<0: a = m return (a+b)/2 Below are five pieces of code, each of which calls this bisection function, and some of which depend on some variable y, that has already been assigned to some fixed integer. Match each piece of code with the value that it produces. bisection (lambda x: x**2-14*x+y, 7, 10, 100) (lambda y: bisection (lambda x: x**2-14*x+y, 7, 10, 100)) (47) bisection (lambda x: x**2-14x+y, 7, 10, 5) bisection (lambda x: 5000x-42071, 7, 10, 100) bisection (lambda x: x**2-14*x+y, 4, 7, 100) Choose... Choose... 8.732050807568877 8.734375 8.414213562373094 5.2679491924311215 8.414200000000001

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter6: Modularity Using Functions

Section6.4: A Case Study: Rectangular To Polar Coordinate Conversion

Problem 9E: (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by...

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(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.
(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:
(Numerical) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is A=s(sa)(sb)(sc) where s=(a+b+c)2 Write, test, and execute a function that accepts the values of a, b, and c as parameters from a calling function, and then calculates the values of sand[s(sa)(sb)(sc)]. If this quantity is positive, the function calculates A. If the quantity is negative, a, b, and c do not form a triangle, and the function should set A=1. The value of A should be returned by the function.
(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?
Mark the following statements as true or false: a. To use a predefined function in a program, you need to know only the name of the function and how to use it. (1) b. A value-returning function returns only one value. (2, 3) c. Parameters allow you to use different values each time the function is called. (2, 7, 9) d. When a return statement executes in a user-defined function, the function immediately exits. (3, 4) e. A value-returning function returns only integer values. (4) f. A variable name cannot be passed to a value parameter. (3, 6) g. If a C++ function does not use parameters, parentheses around the empty parameter list are still required. (2, 3, 6) h. In C + + , the names of the corresponding formal and actual parameters must be the same. (3, 4, 6) i. A function that changes the value of a reference parameter also changes the value of the actual parameter. (7) j. Whenever the value of a reference parameter changes, the value of the actual parameter changes. (7) k. In C++, function definitions can be nested; that is, the definition of one function can be enclosed in the body of another function. (9) l. Using global variables in a program is a better programming style than using local variables, because extra variables can be avoided. (10) m. In a program, global constants are as dangerous as global variables. (10) n. The memory for a static variable remains allocated between function calls. (11)
(Numerical) a. The following is an extremely useful programming algorithm for rounding a real number to n decimal places: Step 1: Multiply the number by 10n Step 2: Add 0.5 Step 3: Delete the fractional part of the result Step 4: Divide by 10n For example, using this algorithm to round the number 78.374625 to three decimal places yields: Step1:78.374625103=78374.625 Step2:78374.625+0.5=78375.125 Step3:Retainingtheintegerpart=78375Step4:78375dividedby103=78.375 Using this algorithm, write a C++ function that accepts a user-entered value and returns the result rounded to two decimal places. b. Enter, compile, and run the program written for Exercise 11a.
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.)
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)