Write a program that reads in a sentence of up to 100 characters and outputs the sentence with spacing corrected and with letters corrected for capitalization. In other words, in the output sentence, all strings of two or more blanks should be compressed to a single blank. All the words in the sentence should start with an uppercase. Treat a line break as if it were a blank space, in the sense that a line break and any number of blank spaces are compressed to a single blank space. Assume that the sentence ends with a period and contains no other periods. For example, the input

Write a program called assignment3 (saved in a file assignment3.java) that computes the greatest common divisor of two given integers. one of the oldest numerical algorithms was described by the greek mathematician, euclid, in 300 b.c. it is a simple but very e↵ective algorithm that computes the greatest common divisor of two given integers. for instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. we will denote the greatest common divisor of x and y as gcd(x, y). the algorithm is based on the clever idea that the gcd(x, y) = gcd(x ! y, y) if x > = y and gcd(x, y) = gcd(x, y ! x) if x < y. the algorithm consists of a series of steps (loop iterations) where the “larger” integer is replaced by the di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

Suppose s, t, and w are strings that have already been created inside main. write a statement or statements, to be added to main, that will determine if the lengths of the three strings are in order by length, smallest to largest. that is, your code should determine if s is strictly shorter than t, and if t is strictly shorter than w. if these conditions hold your code should print (the boolean value) true. if not, your code should print false. (strictly means: no ties) example: if s, t, and w are "cat", "hats", and "skies" your code should print true - their lengths are 3-4-5; but if s, t, and w are "cats" "shirt", and "trust", then print false - their lengths are 4-5-5 enter your code in the box below

The value of sin(x) (in radians) can be approximated by the alternating infinite series create a function (prob3_2) that takes inputs of a scalar angle measure (in radians) and the number of approximation terms, n, and estimates sin(x). do not use the sin function in your solution. you may use the factorial function. though this can be done without a loop (more efficiently), your program must use (at least) one. you may find the mod() function useful in solving the problem.