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All Rights Reserved. 89523810 ... 14159000 ... 55 (Pythagorean Triples) A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse. Find all Pythagorean triples for side1, side2 and hypotenuse all no larger than 500. Use a triple-nested for-loop that tries all possibilities.

Pronounced “n factorial”) and is defined as follows: n! = n · (n - 1) · (n - 2) · … · 1 (for values of n greater than or equal to 1) and n! = 1 (for n = 0). For example, 5! = 5 · 4 · 3 · 2 · 1, which is 120. a) Write a program that reads a nonnegative integer and computes and prints its factorial. b) Write a program that estimates the value of the mathematical constant e by using the formula: e = 1 + -1-- + -1-- + -1-- + … 1! 2! 3! c) Write a program that computes the value of e x by using the formula 2 3 e x = 1 + --x- + x--- + x--- + … 1!

47 Extra Credit Solution #include using std::cout; using std::endl; int main() { int row, column, space; for ( row = 1; row <= 10; ++row ) { // part a for ( column = 1; column <= row; ++column ) ©2000. Deitel & Associates, Inc. and Prentice Hall. All Rights Reserved. 48 One interesting application of computers is drawing graphs and bar charts (sometimes called “histograms”). Write a program that reads five numbers (each between 1 and 30). For each number read, your program should print a line containing that number of adjacent asterisks.