Exercise 6.2 (Completed)

1. (Modify) Rewrite Program 6.4 so that the findMax() function accepts two double-precision
arguments and returns a double-precision value to main(). Make sure to modify main() to
pass two double-precision values to findMax() and to accept and store the double-precision
value returned by findMax().

#include <iostream>
using namespace std;

double findMax(double, double); // the function prototype
int main()
{
	double firstnum, secnum, max;
	cout << "\nEnter a number : ";
	cin >> firstnum;
	cout << "Great!Please enter a second number : ";
	cin >> secnum;
	max = findMax(firstnum, secnum); // the function is called here
	cout << "\nThe maximum of the two numbers is " << max << endl;
	
	system("PAUSE");
	return 0;
	
}
double findMax(double x, double y)
{                     // start of function body
	double maxnum;         // variable declaration
	if (x >= y)         // find the maximum number
		maxnum = x;
	else
		maxnum = y;
	return maxnum;      // return statement
}

2. (Practice) Write function headers for the following functions:
a. A function named check(), which has three parameters. The first parameter should accept
an integer number, the second parameter a floating-point number, and the third parameter
a double-precision number. The function returns no value.

void check(int num1, float num2, double num3)

b. A function named findAbs() that accepts a double-precision number passed to it and
returns that number’s absolute value

double findAbs(double x)

c. A function named mult() that accepts two floating-point numbers as parameters, multiplies
these two numbers, and returns the result.

float mult(float first, float second)

d. A function named square() that computes and returns the square of the integer value
passed to it.

int square(int number)

e. A function named powfun() that raises an integer number passed to it to a positive integer
power (also passed as an argument) and returns the result as an integer.

int powfun(int num, int exponent)

f. A function named table() that produces a table of numbers from 1 to 10, their squares, and
their cubes. No arguments are to be passed to the function, and the function returns no value.

void table(void) or void table()

3. (Program) a. Write a function named rightTriangle() that accepts the lengths of two sides
of a right triangle as the arguments a and b. The subroutine should determine and return the
hypotenuse, c, of the triangle. (Hint: Use Pythagoras’ theorem, c2 = a2 + b2.)

double rightTriangle(double a, double b)
  {
    return sqrt((a * a) + (b * b));
  }
  
b. Include the function written for Exercise 3a in a working program. The main() function
should call rightTriangle() correctly and display the value the function returns. Test the
function by passing various data to it and verifying the returned value.

#include <math.h>  
#include <cmath>
#include <iostream>
using namespace std;

double rightTriangle(double, double); // the function prototype
int main()
{
	double num,num2;
	cout << "Enter your number" << endl;
	cin >> num;
	cout << "Enter your other number" << endl;
	cin >> num2;
	cout << "The sqrt is  " << rightTriangle(num,num2) << endl;
	
	system("PAUSE");
	return 0;
	
}
double rightTriangle(double a, double b)
{
	
	return sqrt((a*a) + (b*b));
}

4. (Program) a. Write a C++ function named findAbs() that accepts a double-precision number
passed to it, computes its absolute value, and returns the absolute value to the calling
function. A number’s absolute value is the number itself if the number is positive and the
negative of the number if the number is negative.

double findAbs(double number)
  {
    if(number < 0)
      number = -number;
    return number;
  }

b. Include the function written in Exercise 4a 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 and
verifying the returned value.

double findAbs(double); // the function prototype
int main()
{
	double number;
	cout << "Enter your number" << endl;
	cin >> number;
	cout << "The number is now positve " << findAbs(number) << endl;
	
	system("PAUSE");
	return 0;
	
}
double findAbs(double number)
{
	if (number < 0)
		number = -number;
	return number;
}
5. (Program) a. The volume, V, of a cylinder is given by the formula
V = π r^2 L
where 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.

double cylvol(double r, double L)
{
	double volume = 3.1416 * pow(r, 2)*L;
	
	return 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 and
verifying the returned value.
#include <cmath>
#include <iostream>
using namespace std;

double cylvol(double, double); // the function prototype
int main()
{
	double num,num2;
	cout << "Enter your number" << endl;
	cin >> num;
	cout << "Enter your other number" << endl;
	cin >> num2;
	cout << "The volume of a cylinder is  " << cylvol(num,num2) << endl;
	
	system("PAUSE");
	return 0;
	
}
double cylvol(double r, double L)
{
	double volume = 3.1416 * pow(r, 2)*L;
	
	return volume;
}

6. (Program) a. The surface area, S, of a cylinder is given by the formula
S = 2 π r l
where r is the cylinder’s radius, and l is the length of the cylinder. Using this formula, write a
C++ function named surfarea() that accepts a cylinder’s radius and length and returns its
surface area.

double surfarea(double r, double l)
{
	double surf = 2 * 3.14 * r * l;
	

return surf;
}

b. Include the function written in Exercise 6a 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 and
verifying the returned value.

#include <iostream>
using namespace std;

double surfarea(double, double); // the function prototype
int main()
{
	double num,num2;
	cout << "Enter your number" << endl;
	cin >> num;
	cout << "Enter your other number" << endl;
	cin >> num2;
	cout << "The volume of a cylinder is  " << surfarea(num,num2) << endl;
	
	system("PAUSE");
	return 0;
	
}
double surfarea(double r, double l)
{
	double surf = 2 * 3.14 * r * l;
	
	return surf;
}

7. (Program) a. Write a function named totamt() that uses four parameters named quarters,
dimes, nickels, and pennies, which represent the number of each of these coins in a piggybank.
The function should determine the dollar value of the number of quarters, dimes,
nickels, and pennies passed to it and return the calculated value.

double totamt(double quarters, double dimes, double nickels, double pennies)
{
	double value = (quarters * .25) + (dimes * .10) + (nickels * .05) + (pennies * .01);
	
	return value;
}

b. Include the function written in Exercise 7a 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 and
verifying the returned value.

#include <iostream>
using namespace std;

double totamt(double, double,double,double); // the function prototype
int main()
{
	double num,num2,num3,num4;
	cout << "Enter your number" << endl;
	cin >> num;
	cout << "Enter your other number" << endl;
	cin >> num2;
	cout << "Enter your third number" << endl;
	cin >> num3;
	cout << "Enter your forth number" << endl;
	cin >> num4;
	cout << "The volume of a cylinder is  " << totamt(num,num2,num3,num4) << endl;
	
	system("PAUSE");
	return 0;
	
}
double totamt(double quarters, double dimes, double nickels, double pennies)
{
	double value = (quarters * .25) + (dimes * .10) + (nickels * .05) + (pennies * .01);
	
	return value;
}

8. (Program) a. Write a function named daycount() that accepts a month, day, and year as its
input arguments; calculates an integer representing the total number of days from the turn of
the century to the date that’s passed; and returns the calculated integer to the calling function.
For this problem, assume each year has 365 days and each month has 30 days. Test your function
by verifying that the date 1/1/00 returns a day count of 1.

double daycount(int month, double day, double year)
{
	if (month % 30 == 0){
		month = 30;
	}
	else if (month == 1){
		month = 0;
	}
	else{ month = month * 30;}

	double value = (day)+(month)+(year*365);

		return value;
}

b. Include the daycount() function written for Exercise 8a in a working program. The
main() function should correctly call daycount() and display the integer returned by the
function. Test the function by passing various data to it and verifying the returned value.

#include <iostream>
using namespace std;

double daycount(int, double,double); // the function prototype
int main()
{
	double num,num2,num3;
	cout << "Enter your month" << endl;
	cin >> num;
	cout << "Enter your day " << endl;
	cin >> num2;
	cout << "Enter the year" << endl;
	cin >> num3;
	cout << "The total number of day passed sence the first of the year" << daycount(num,num2,num3) << endl;
	
	system("PAUSE");
	return 0;
	
}
double daycount(int month, double day, double year)
{
	if (month % 30 == 0){
		month = 30;
	}
	else if (month == 1){
		month = 0;
	}
	else{ month = (month-1) * 30;} // only one I needed *facepam* lol

	double value = (day)+(month)+(year*365);

		return value;
}

9. (Program) a. A clever and simple method of preparing to sort dates into ascending (increasing)
or descending (decreasing) order is to convert a date in the form month/day/year into an
integer number with the formula date = year × 10000 + month × 100 + day. For example, using
this formula, the date 12/6/1999 converts to the integer 19991206, and the date 2/28/2011 converts
to the integer 20110228. Sorting the resulting integer numbers puts dates into the correct
order automatically. Using this formula, write a function named convertdays() that accepts
a month, day, and year; converts the passed data into a single date integer; and returns the
integer to the calling function.

int convertdays(int month, int day, int year)
{

	int date = year * 10000 + month * 100 + day;

		return date;
}

b. Include the convertdays() function written for Exercise 9a in a working program. The
main() function should call convertdays() correctly and display the integer the function
returns. Test the function by passing various data to it and verifying the returned value.

#include <iostream>
using namespace std;

int convertdays(int, int, int); // the function prototype
int main()
{
	int num,num2,num3;
	cout << "Enter your month" << endl;
	cin >> num;
	cout << "Enter your day " << endl;
	cin >> num2;
	cout << "Enter the year" << endl;
	cin >> num3;
	cout << "The total number of day passed sence the first of the year" << convertdays(num,num2,num3) << endl;
	
	system("PAUSE");
	return 0;
	
}
int convertdays(int month, int day, int year)
{

	int date = year * 10000 + month * 100 + day;

		return date;
}

10. (Program) a. Write a function named ReadOneChar() that reads a key pressed on the keyboard
and displays the integer code of the entered character.

int ReadOneChar(char reads)
{
return reads;
}

b. Include the ReadOneChar() function written for Exercise 10a in a working program. The
main() function should correctly call ReadOneChar() and display the integer the function
returns. Test the function by passing various data to it and verifying the returned value.

#include <iostream>
using namespace std;

int ReadOneChar(char); // the function prototype
int main()
{
	char one;
	cout << "Enter your character" << endl;
	cin >> one;
	cout << "The key pressed was " << ReadOneChar(one) << endl;

	
	system("PAUSE");
	return 0;
	
}
int ReadOneChar(char reads)
{
		return reads;
}

11. (Program) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is

A  =[s(s)(s-a)(s-b)(s-c)]
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 s and [s(s - a)(s - b)(s - c)]. 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. Test
the function by passing various data to it and verifying the returned value.

#include <iostream>
using namespace std;

int HeronForm(int,int,int); // the function prototype
int main()
{
	int s,a,b,c;
	
	cout << "Enter a" << endl;
	cin >> a;
	cout << "Enter b" << endl;
	cin >> b;
	cout << "Enter c" << endl;
	cin >> c;
	cout << "The Heron's Area is  " << HeronForm( a, b, c) << endl;

	
	system("PAUSE");
	return 0;
	
}
int HeronForm( int a, int b, int c)
{
	int Area;

	int s = ((a + b + c) / 2);
	Area = (s*(s)*(s - a)*(s - b)*(s - c));


	if ((Area == -(Area))){
		Area = -1;
	}

		return Area;
}

12. (Program) a. Write a function named whole() that returns the integer part of any number
passed to the function. (Hint: Assign the passed argument to an integer variable.)

int whole( int a)
{
		return a;
}

b. Include the function written in Exercise 12a 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 and
verifying the returned value.

#include <iostream>
using namespace std;

int whole(int); // the function prototype
int main()
{
	int s,a,b,c;
	
	cout << "Enter a" << endl;
	cin >> a;
	
	cout << "The integer part of any number is  " << whole(a) << endl;

	
	system("PAUSE");
	return 0;
	
}
int whole( int a)
{
		return a;
}

13. (Program) a. Write a C++ function named fracpart() that returns the fractional part of any
number passed to it. For example, if the number 256.879 is passed to fracpart(), the number
0.879 should be returned. Have fracpart() call the whole() function you wrote in
Exercise 12. The number returned can then be determined as the number passed to
fracpart() less the returned value when the same argument is passed to whole(). The
completed program should consist of main() followed by fracpart() followed by whole().

double fracpart( double a)
{
	double b;
	double frac=modf(a, &b);
		return frac;
}

b. Include the function written in Exercise 13a 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 and
verifying the returned value.

#include <iostream>
using namespace std;

double fracpart(double); // the function prototype
int main()
{
	double a;
	
	cout << "Enter a" << endl;
	cin >> a;
	
	cout << "The integer part of any number is  " << fracpart(a) << endl;

	
	system("PAUSE");
	return 0;
	
}
double fracpart( double a)
{
	double b;
	double frac=modf(a, &b);
		return frac;
}

14. (Program) a. Years that are evenly divisible by 400 or are evenly divisible by 4 but not by 100
are leap years. For example, because 1600 is evenly divisible by 400, 1600 was a leap year.
Similarly, because 1988 is evenly divisible by 4 but not by 100, it was also a leap year. Using
this information, write a C++ function that accepts the year as user input and returns a 1 if the
passed year is a leap year or a 0 if it isn’t.

int leapyear( int num)
{

	if (num % 4 == 0 && num % 100 != 0){
		num = 1;
	}
	else{ num = 0; }
		return num;
}

b. Include the function written in Exercise 14a 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 and
verifying the returned value.

#include <iostream>
using namespace std;

int leapyear(int); // the function prototype
int main()
{
	int a;
	
	cout << "Enter a" << endl;
	cin >> a;
	
	cout << "The integer part of any number is  " << leapyear(a) << endl;

	
	system("PAUSE");
	return 0;
	
}
int leapyear( int num)
{

	if (num % 4 == 0 && num % 100 != 0){
		num = 1;
	}
	else{ num = 0; }
		return num;
}

15. (Program) a. A second-degree polynomial in x is given by the expression ax2 + bx + c, where a,
b, and c are known numbers and a is not equal to 0. Write a C++ function named polyTwo
(a,b,c,x) that computes and returns the value of a second-degree polynomial for any passed
values of a, b, c, and x.

int polyTwo( int a, int b, int c, int x)
{

	int poly = a*pow(x, 2) + b*x + c;

		return poly;
}

b. Include the function written in Exercise 15a 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 and
verifying the returned value.

#include <cmath>
#include <iostream>
using namespace std;

int polyTwo(int,int,int,int); // the function prototype
int main()
{
	int a,b,c,x;
	
	cout << "Enter a" << endl;
	cin >> a;
	cout << "Enter b" << endl;
	cin >> b;
	cout << "Enter c" << endl;
	cin >> c;
	cout << "Enter x" << endl;
	cin >> x;
	cout << "The second polynomical is  " << polyTwo(a,b,c,x) << endl;

	
	system("PAUSE");
	return 0;
	
}
int polyTwo( int a, int b, int c, int x)
{

	int poly = a*pow(x, 2) + b*x + c;

		return poly;
}

16. (Program) a. The following is a useful programming algorithm for rounding a real number to
n decimal places:
Step 1: Multiply the number by 10^n.
Step 2: Add 0.5.
Step 3: Delete the fractional part of the result.
Step 4: Divide by 10^n.
For example, using this algorithm to round the number 78.374625 to three decimal places
yields:
Step 1: 78.374625 × 10^3 = 78374.625
Step 2: 78374.625 + 0.5 = 78375.125
Step 3: Retaining the integer part = 78375
Step 4: 78375 divided by 10^3 = 78.375
Using this algorithm, write a C++ function that accepts a user-entered value and returns the
result rounded to two decimal places.

double realTwoNum(double num, int& num2)
{
	num=(num * pow(10, 2));

	num = num + .5;
	num2 = (int) num;
	double done = (num2 / pow(10, 2));

		return done;
}

b. Include the function written in Exercise 16a 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 and
verifying the returned value.

#include <cmath>
#include <iostream>
using namespace std;

double realTwoNum(double,int&); // the function prototype
int main()
{
	double num;
	int num2;
	
	cout << "Enter a" << endl;
	cin >> num;
	
	cout << "The number with two decimal places  " << realTwoNum(num,num2) << endl;

	
	system("PAUSE");
	return 0;
	
}
double realTwoNum(double num, int& num2)
{
	num=(num * pow(10, 2));

	num = num + .5;
	num2 = (int) num;
	double done = (num2 / pow(10, 2));

		return done;
}