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operator % for the division of a negative integer by a positive integer. See Problem 3.16 and Example 1.16.

3.52 3.53

Fig. 2-20

Remember that Int produces a value whose magnitude is equal to or smaller than its argument if the argument is positive, and equal to or larger (in magnitude) than its argument if the argument is negative.

Redo Problem 319 using a do whi le loop instead of the whi le loop Write and run a program that directly implements the quotient operator / and the remainder operator % for the division of any integer (positive, negative, or zero) by any nonzero integer See Problem 316 and Problem 35 1 Modify the Integer Square Root program in Problem 315 so that it runs more efficiently Use the Binary Search Algorithm in place of the Linear Search Algorithm First see if the given positive integer x is less than 9; if it isn t, output either 0 (if x < 1) or 1 (if x < 4) or 2, and return If x 2 9, then its integer square root is between 2 and x/2 Split that interval, and then compare x with n*n where n is the midpoint of that interval.

(a) Postulate 17. (b) Postulate 18. (c) Postulate 14. (d) Postulate 13. (AC is less than the sum of AB and BC.)

Use the comparison to determine in which half of the interval the solution lies Repeat the process on that subinterval Use only integers for the endpoints and midpoints of the intervals When the midpoint is 1 more than its left endpoint, it will be the solution Modify the program in Example 314 so that it prints the precision and magnitude range of the double type Modify the Quadratic Equation program in Problem 220 so that it prints the equation in a form more like that used in mathematics For example, if a is 1, b is 0, and c is -3, then it would print XQ - 3 = 0 insteadof lx*2 + OX + -3 = 0 Modify the Quadratic Equation program in Problem 220 so that it correctly handles the special cases where a = 0, b = 0, and/or c = 0.

A theorem is a statement, which, when proved, can be used to prove other statements or derive other results. Each of the following basic theorems requires the use of definitions and postulates for its proof. Note: We shall use the term principle to include important geometric statements such as theorems, postulates, and definitions.

For example, it would report that the 125 is the solution to 4x - 5 = 0, that 0 is the solution to 4x = 0, that there is no solutions to 5 = 0, and that all reals are solutions to 0 = 0 Write and test a program that inputs 3 positive integers day, month, and year, and then prints the date that they represent, the number of days in that month, and a statement about whether that year is a leap year For example, if the 3 inputs are 6, 4, and 1997, then the program would print Apri 1 6, 1997 (for4/6/97), April has 30 days, and 1997 is not.

PRINCIPLE 1:

Write and test a program that inputs 4 positive integers day, month, year, and days, and then prints two dates, the date represented by the given day, month, and year, and the date that occurs days later. For example, if the 4 inputs are 6,4, 1997, and 100, then the two dates printed would be Apri 1 6, 19 97 (for 4/6/97), and JULY 15, 19 97 (for 4/6/97 + 100 days). Modify the Linear Regression program (Problem 3.20) so that, after computing the equation of the regression line, it allows the user to interpolate by inputting x-values and outputting the corresponding y-values computed from the equation. Modify the Monte Hall game (Problem 3.22) so that the user can play the game repeatedly in a single run of the program. Count the number of times the player wins, and print the percentage of wins at the end of the program.