Suppose we need to construct a tin can with a fixed volume V cm3 in the shape of a cylinder with radius r cm and height h cm. (Here V should be regarded as a constant. In some sense, your answers should be independent of the exact value of V .) The can is made from 3 pieces of metal: a rectangle for the side and two circles for the top and bottom. Suppose that these must be cut out of a rectangular sheet of metal. Our goal is to find the values of r and h, and the dimensions of this rectangular sheet that minimize its area.

1. Draw a picture of how the rectangle and two circles could be cut out of a larger rectangle. There are multiple ways to do this (I can think of at least 3). Draw as many as you can, solve the problems below for each arrangement and then compare your answers.

2. Label the sides of the rectangle in terms of r and h. Express the rectangle’s area in terms of r and h. Also, note whether there are any assumptions about r and h that you need to make in order for your picture to make sense. (For example, if you draw a circle with diameter 2r inside of a rectangle with side l, then you must have 2r ≤ l.)

3. Use the fact that the can’s volume is V = πr2h to express h in terms of r, and write the rectangle’s area as a function of r. (Or else, you may alternatively solve for r and write the area as a function of h.)

4. Find the value of r (or h) that minimizes the rectangle’s area. What is the correspond- ing value of h (or r), and the dimensions of the rectangle? Your answers will most likely be in terms of V , but the ratio h/r might be a number. What is the minimum area of the rectangle in terms of V ?

5. As mentioned above, you should complete (1)-(4) for as many different arrangements as you can think of. (The math for some might be very simple.) Then compare your answers to find the best way of arranging the 2 circles and rectangle inside the larger rectangle, and the minimum possible area of the rectangle.

6. What if you need to make 2 (or more) cans in the same way. Can you find an arrangement of all the necessary pieces inside a single rectangle that is even more efficient?

package SOLUTION;

import java.util.Collection;
import java.util.Set;

public interface MapInterface<K, V> {
  
   /**
   * If the given key is not already in the map, adds the
   * key-value pair to the map. Otherwise, updates the old
   * value of the existing key to the specified value.
   * @param key the key
   * @param value the value to be stored in the map with the key
   * @return null if the key was not already in the map, or
   * the old value associated with the key if the key was already in the map
   */
   public V put(K key, V value);
  
   /**
   * Gets the value from the map that is associated with the given key
   * @param key the key
   * @return the value associated with the key, or null if the key is
   * not in the map
   */
   public V get(K key);
  
   /**
   * Removes from the key-value pair associated with the specified key
   * @param key the key
   * @return the value associated with the key, or null if the key is
   * not in the map
   */
   public V remove(K key);
  
   /**
   * Returns whether the map contains the key-value pair associated with
   * the specified key
   * @param key the key
   * @return true if the map contains a key-value pair with the specified
   * key, and false otherwise
   */
   public boolean containsKey(K key);
  
   /**
   * Returns whether the map contains no elements
   * @return true if the map contains no key-value pairs, and false otherwise
   */
   public boolean isEmpty();
  
   /**
   * Removes all elements from the map
   */
   public void clear();
  
   /**
   * Gets the number of key-value pairs in the map
   * @return the number of key-value pairs in the map
   */
   public int size();
  
   /**
   * Gets a set of all keys in the map
   * @return
   */
   public Set<K> keySet();

   /**
   * Gets a set of all values in the map
   * @return
   */
   public Collection<V> values();

}

package SOLUTION;
public class Tester {

   public static void main(String[] args) {
       ArrayListMap<String, Integer> alm = new ArrayListMap<String, Integer>();
      
       System.out.println(alm.put("Cindy", 1));
       System.out.println(alm.put("Nina", 2));
       System.out.println(alm.put("Morgan", 3));
       System.out.println(alm.put("Michael", 4));
      
       System.out.println(alm.size());
       System.out.println(alm.containsKey("Morgan"));
       System.out.println(alm.containsKey("Jack"));
       System.out.println(alm.get("Michael"));
       System.out.println(alm.values());
       System.out.println(alm.keySet());
       System.out.println(alm.put("Michael", 6));
       System.out.println(alm.get("Michael"));
       System.out.println(alm.remove("Michael"));
       System.out.println(alm.remove("Morgan"));
       System.out.println(alm.remove("Nina"));
       System.out.println(alm.remove("Cindy"));
       System.out.println(alm.size());
   }
  
}

[The following information applies to the questions displayed below.]

In 2021, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2023. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

2-a. In the journal below, complete the necessary journal entries for the year 2021 (credit "Various accounts" for construction costs incurred).
2-b. In the journal below, complete the necessary journal entries for the year 2022 (credit "Various accounts" for construction costs incurred).
2-c. In the journal below, complete the necessary journal entries for the year 2023 (credit "Various accounts" for construction costs incurred).

Record construction costs.

Record progress billings.

Record cash collections.

Record gross profit (loss).

Bark beetles are tiny insects with hard, cylindrical bodies that reproduce under the bark of trees. While bark beetles are native to U.S. forests and play important ecological roles, they can cause extensive tree mortality and negative economic and social impacts. Researchers at Los Alamos National Laboratory are interested in the behavior of Bark Beetles living in the Santa Fe National Forest. In particular, they are interested in the average size of these beetles (body length measured in mm). They assume that the distribution of body length for these beetles can be modeled with a Normal distribution with mean μ and standard deviation σ. After spending several weeks in the field, they have measured and recorded the body length of 263 of these beetles. The average body length of these 263 beetles is 6.14mm with a calculated standard deviation of 1.89mm.

1. What is the population of interest?

2. What is the sample size?

3. What is the sample?

4. What parameters are mentioned in this problem? Explain what the parameters mean in terms of the problem.

5. What is the sample data?

6. What are the estimators mentioned in this problem? For each estimator, explain which parameter it is supposed to estimate.

7. What are the estimates for the parameters in this problem?

• What are the roots of the brachial plexus?
• What are the major nerves (Terminal nerves) of the brachial plexus?
• What are the roots of the long thoracic nerve?
• Name 5 muscles that are innervated by the radial nerve
• Name 5 muscles that are innervated by the mdian nerve
• Name 5 muscles that are innervated by the ulnar nerve

Write a program in java which is in main and uses no classes, methods, loops or if statements Ask the user to enter their first name Ask the user to enter their last name Print their initials followed by periods (ie. Clark Kent = C. K.) Print the number of letters in their last name

Linux Directories, File Properties, and the File System in C

Understanding Unix/Linux Programming

Your version of mv command

1. The mv command is more than just a wrapper around the rename system call. Write a version of mv that accepts two argument. The first argument must be the name of a file, and the second argument may be the name of a file or the name of a directory. If the destination is the name of a directory, then mv moves the file into that directory. Otherwise mv rename the file if possible.
2. Add comments to code.

Linux Directories, File Properties, and the File System in C

Code your version of mv command in C

1. The mv command is more than just a wrapper around the rename system call. Write a version of mv that accepts two argument. The first argument must be the name of a file, and the second argument may be the name of a file or the name of a directory. If the destination is the name of a directory, then mv moves the file into that directory. Otherwise mv rename the file if possible.
2. Add comments to code.

Create a program using Java.

Create two different 3D arrays with random numbers. (lets name them array1 and array 2)

Add the two 3Darrays together and then get the average.

Save the average on a separate 3D array.(lets name it array3)

Then add array1 and array3 then get the average

Save the average on a separate 3Darray(lets name it array 4)

Then add array2 and array3 then get the average

Save the average on a separate 3Darray (lets name it array5)

Use recursion