After the break statement in (a) is executed in the following loop, which statement is executed? Show the output. After the continue statement in (b) is executed in the following loop, which statement is executed? Show the output.

a.

for(int i = 1; i < 4; i++) {
  for(int j = 1; j < 4; j++) {
    if(i * j > 2)
      break;
    System.out.println(i * j);
  }
  System.out.println(i);
}

b.

for(int i = 1; i < 4; i++) {
  for(int j = 1; j < 4; j++) {
    if(i * j > 2)
      continue;
    System.out.println(i * j);
  }
  System.out.println(i);
}

Let k be a fixed positive integer and let G = (V, E) be a loop-free undirected graph, where $\operatorname{deg}(\mathrm{v}) \geq \mathrm{k}$ for all $\mathrm{v} \in \mathrm{V}.$ Prove that G contains a path of length k.

Choose a word or words from the box below to complete the following sentence.

Fish ________________ systems pump blood in a single loop through a heart with two main chambers.

Draw the circuit diagram of the basic inverting amplifier configuration. Give an expression for the closed-loop voltage gain of the circuit in terms of the resistances, assuming an ideal op amp. Give expressions for the input impedance and output impedance of the circuit.

Write a program with a loop that asks the user to enter a series of positive numbers. The user should enter a negative number to signal the end of the series. After all the positive numbers have been entered, the program should display their sum.

Sort the following list using the bubble sort algorithm as discussed in this chapter. Show the list after each iteration of the outer for loop. 82, 17, 40, 28, 15, 55, 46, 93, 6, 67, 11, 3

After the break statement in (a) is executed in the following loop, which statement is executed? Show the output. After the continue statement in (b) is executed in the following loop, which statement is executed? Show the output.

(a)

for (int i = 1; i < 4; i++) {
 for (int j = 1; j < 4; j++) {
  if (i * j > 2) 
    break;
  System.out.println(i * j);
 }
 System.out.println(i);
}

(b)

for (int i = 1; i < 4; i++) {
  for (int j = 1; j < 4; j++) {
    if (i * j > 2) 
       continue;
    System.out.println(i * j);
 }
 System.out.println(i);
}

A car in an amusement park ride rolls without friction around the track shown in Fig. . It starts from rest at point $A$ at a height $h$ above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of $h$ (in terms of $R$ ) such that the car moves around the loop without falling off at the top (point $B$ )? (b) If $h=3.50 R$ and $R=20.0 \mathrm{~m}$, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point $C$, which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale.

** A Game of Twenty-One**

For this assignment, you will write a program that lets the user play against the computer in a variation of the popular blackjack card game. In this variation of the game, two six-sided dice are used instead of cards. The dice are rolled, and the player tries to beat the computer's hidden total without going over 21. Here are some suggestions for the game's design:

• Each round of the game is performed as an iteration of a loop that repeats as long as the player agrees to roll the dice, and the player's total does not exceed 21.
• At the beginning of each round, the program will ask the user whether or not he or she wants to roll the dice to accumulate points.
• During each round, the program simulates the rolling of two six-sided dice. It rolls the dice first for the computer, and then it asks the user whether he or she wants to roll. (Use the Die class that was shown in Code Listing 6-14 to simulate the dice.)
• The loop keeps a running total of both the computer's and the user's points.
• The computer's total should remain hidden until the loop has finished.
• After the loop has finished, the computer's total is revealed, and the player with the most points, without going over 21, wins.

Exercises refer to the following algorithm segment. For each positive integer n, let

$$a_n$$

be the number of iterations of the while loop. while (n>0), n :=n div 2, end while. Trace the action of this algorithm segment on n when the initial value of n is 27.

In a program you need to store the populations of $12$ countries.

a. Define two arrays that may be used in parallel to store the names of the countries and their populations.

b. Write a loop that uses these arrays to print each country’s name and its population.n 3(a).

A single circular loop of wire of radius $r=2.0 \mathrm{~cm}$ rotates at a frequency of $60 \mathrm{~Hz}$ in a constant magnetic field of magnitude $B=1.5 \mathrm{~T}$. What is the approximate maximum emf induced in this generator?

A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sitting in the loop with the rope hanging vertically when the child's father pulls on the child with a horizontal force and displaces the child to one side. Just before the child is released from rest, the rope makes an angle of $15^{\circ}$ with the vertical and the tension in the rope is $280 \mathrm{~N}$. If the maximum horizontal force the father can exert on the child is $93 \mathrm{~N}$, what is the maximum angle with the vertical the rope can make while the father is pulling horizontally?

Each exchange operation on line 5 of HEAP-INCREASE-KEY typically requires three assignments. Show how to use the idea of the inner loop of INSERTION-SORT to reduce the three assignments down to just one assignment.