The Card Box Problem C++ you should write documentation for your program.    Using functions, write a program that prompts the user to enter the area of the flat cardboard. The program then outputs the length and width of the cardboard and the length of the side of the square to be cut from the corner so that the resulting box is of maximum volume. Calculate your answer to three decimal places. Your program must contain a function that takes as input the length and width of the cardboard and returns the side of the square that should be cut to maximize the volume. The function also returns the maximum volume.

(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.

(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

(General math) a. The volume, V, of a cylinder is given by this formula: V=r2L r is the cylinder’s radius, and L is its length. Using this formula, write a C++ function named cylvol() that accepts a cylinder’s radius and length and returns its volume. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main() and returns a value to main() correctly. Have main() use a cout statement to display the returned value. Test the function by passing various data to it.

Why do you need to include function prototypes in a program that contains user-defined functions? (5)

(Physics) Buoyancy is the upward force a liquid exerts on a submerged object, as shown in Figure 6.9. The buoyancy force is given by this formula: B=pgV Bisthebuoyancyforce( lbforN).isthefluiddensity( slug/f t 3 orkg/ m 3 ).gistheaccelerationcausedbygravity( 32.2ft/se c 2 or9.8m/ s 2 ).Vistheobjectsvolume( f t 3 or m 3 ). a. Using this formula, write a function named buoyantForce(double ro, double vol, int units) that accepts a fluid density, the volume of an object placed in the fluid, and the units to be used(1=U.S.Customaryunits,2=metricunits), and returns the buoyancy force exerted on the object. b. Include the function written for Exercise 6a in a working C++ program, and use your program to complete the following chart:

(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:

Write a program that takes as input five numbers and outputs the mean (average) and standard deviation of the numbers. If the numbers are x1,x2,x3,x4,andx5, then the mean is x=(x1+x2+x3+x4+x5)/5 and the standard deviation is: s=(x1x)2+(x2x)2+(x3x)2+(x4x2)+(x5x2)5 Your program must contain at least the following functions: a function that calculates and returns the mean and a function that calculates the standard deviation.

(Modify) a. Modify the program you wrote for Exercise 7 to provide the mass of a person as an output, given his or her weight as an input to the program. Use your program to determine the mass of a person who weighs 140 lbf on Earth. b. Modify the program written for Exercise 7a to also output the person’s weight on Mars and the moon. The pull of gravity on Mars is 12.54ft/sec2=3.728m/s2,andonthemoonis5.33ft/sec2=1.625m/s2.

4. During each summer, John and Jessica grow vegetables in their backyard and buy seeds and fertilizer from a local nursery. The nursery carries different types of vegetable fertilizers in various bag sizes. When buying a particular fertilizer, they want to know the price of the fertilizer per pound and the cost of fertilizing per square foot. The following program prompts the user to enter the size of the fertilizer bag, in pounds, the cost of the bag, and the area, in square feet, that can be covered by the bag. The program should output the desired result. However, the program contains logic errors. Find and correct the logic errors so that the program works properly. // Logic errors. #include #include using namespace std; int main() { double costs double area; double bagsize; cout > bagsize; cout > cost; cout > area; cout << endl; cout << "The cost of the fertilizer per pound is: $" << bagsize / cost << endl; cout << "The cost of fertilizing per square foot is: $" << area / cost << endl; return 0; }