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##### Computer Science 1620

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**Computer Science 1620**Math Library**Remember this program?**• suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years #include <iostream> using namespace std; int main() { cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years #include <iostream> using namespace std; int main() { double balance = 25000.0; balance = balance * 1.08; cout << "Year 1: $" << balance << endl; balance = balance * 1.08; cout << "Year 2: $" << balance << endl; balance = balance * 1.08; cout << "Year 3: $" << balance << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years #include <iostream> #include <iomanip> using namespace std; int main() { double balance = 25000.0; cout << fixed << showpoint << setprecision(2); balance = balance * 1.08; cout << "Year 1: $" << balance << endl; balance = balance * 1.08; cout << "Year 2: $" << balance << endl; balance = balance * 1.08; cout << "Year 3: $" << balance << endl; return 0; }**Suppose we alter the program?**• suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty yearsc) thirty years**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 20: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08* 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 30: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { double balance = 25000.0; cout << fixed << showpoint << setprecision(2); balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 10: $" << balance << endl; balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 20: $" << balance << endl; balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 30: $" << balance << endl; return 0; }**The previous example worked, but …**• to calculate 1.0830 required that we manuallytype in thirty multiplications • suppose we had wanted to know the balance after 100 years?**pow(b,e)**• to compute b raised to the power of e, one can use the pow function • syntax: • the pow statement itself is an expression • value: the first expression raised to the power of the second expression pow( , ) numeric expression numeric expression**Example:**#include <iostream> #include <cmath> using namespace std; int main() { cout << pow(3.0, 3.0) << endl; cout << pow(3, 4.0) << endl; cout << pow(4.0, 3) << endl; int x = 5; double y = 6.0; cout << pow(x, y) << endl; cout << pow(x, y) + pow(3.0, 3.0) << endl; cout << pow( pow(x, y), pow(3.0, 3.0) ) << endl; return 0; }**A note about pow**• you cannot send it two integer expressions • cout << pow(3, 4) << endl; // compiler error • this has to do with function overloading • we will examine functions later • for now, just know that one expression has to be a floating point type**A Note about Types**• when using a math function (from previous slide), the type of the expression is the same as the type of the input expression, with some exceptions: • an integerexpression is converted to a double • for the pow function, the type of the expression is the largest of the base and exponent expressions • for abs • integers are not converted to doubles • shorts and chars are converted to ints**A Note about the Trig Functions**• the input expression is considered to be radians • hence, sin(30.0) = -0.988032, not 0.5 • to convert radians to degrees, multiply the value by (π / 180)**Example:**#include <iostream> #include <cmath> using namespace std; int main() { const double PI = 3.14159; cout << sin(30) << endl; cout << sin(30 * PI / 180) << endl; return 0; }**Back to our previous example**• suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty yearsc) thirty years**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 20: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 30: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * pow(1.08, 10) << endl; cout << "Year 10: $" << 25000 * pow(1.08, 20) << endl; cout << "Year 10: $" << 25000 * pow(1.08, 30) << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <iomanip> using namespace std; int main() { double balance = 25000.0; cout << fixed << showpoint << setprecision(2); balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 10: $" << balance << endl; balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 20: $" << balance << endl; balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 30: $" << balance << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { double balance = 25000.0; cout << fixed << showpoint << setprecision(2); balance = balance * pow(1.08, 10); cout << "Year 10: $" << balance << endl; balance = balance * pow(1.08, 10); cout << "Year 20: $" << balance << endl; balance = balance * pow(1.08, 10); cout << "Year 30: $" << balance << endl; return 0; }**Suppose that I invest $25000 into a mutual fund that returns**8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirtyyears #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { double balance = 25000.0; double increase = pow(1.08, 10); cout << fixed << showpoint << setprecision(2); balance = balance * increase; cout << "Year 10: $" << balance << endl; balance = balance * increase; cout << "Year 20: $" << balance << endl; balance = balance * increase; cout << "Year 30: $" << balance << endl; return 0; }**Example 2: Suppose you have a cannon. Given an initial**velocity of a cannonball and the angle of the cannon θ, output (1) the time that the ball remains in the air and (2) the maximum height of its trajectory**Arithmetic Data and Operators**• Given a value θ and initial velocity v0, we can calculate the time that the ball stays in the air: • and its maximum height: • g is approximately -9.81 m/s at sea level**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / -9.81; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; } cmath call**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) /-9.81; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; } Magic Number**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) /G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; } Expects radians**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * 3.14159 / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; } Magic Number**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }**Write a program that accepts an initial velocity and the**angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places. #include <iostream> #include <cmath> #include <iomanip> using namespace std; int main() { const double PI = 3.14159; const double G = -9.81; double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(3); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0; }