Which sentence uses a pair of synonyms? Because there was so much shouting, many of the protestors began screaming in order to be heard. Although we were tired after the long hike into the woods, we were still energetic enough to make camp. Despite all the exercise and the healthy eating habits, she still felt sick when she woke up in the morning. The children were too excited about the next day to settle down in their peaceful surroundings.

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.

Robots with telescoping arms are sometimes used to perform tasks (e. g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

Howard is designing a chair swing ride. the swing ropes are 5 meters long, and in full swing they tilt in an angle of 29° outside chairs to be 2.75 m above the ground in full swing.