1. History of computing:

(a) Where does the word "algorithm" come from?

(b) Briefly describe Francois Viete's contributions
to computing.

(c) *For extra credit:* describe one more
event from the history of computing.

(a) The word "algorithm" comes from the name of a scientist Al-Khorezmi, which literally means "from Khorezm"; Khorezm (now called Khiva) is an ancient city in what is now Uzbekistan. In the Middle Ages, Al-Khorezmi wrote a book in which he described all the mathematical methods known at that time: how to divide numbers, how to solve linear equations, how to compute areas, etc. His explanations were so detailed, unambiguous, and clear, that they became a "gold standard" for explanations of different procedures. When someone wanted to praise a step-by-step description for being clear, they would say "This is like in a book by Al-Khorezmi". Eventually, such clear descriptions became known as algorithms. (b) Francois Viete (also known by his Latinized name Francisco Vieta) invented variable. Before this invention, to describe how to compute the area of a triangle, we would need to write "multiply the first side by the second side". More modern notations like A = a * b made computations easier.2. As you may know, this year, the main Independence Day celebration was moved from Mexico City to the city of Dolores Hidalgo about 170 miles away. As a result, some people who planned to celebrate in Mexico City need to travel further away. Suppose that you know the exact distance, you know how much miles per gallon your car makes, and you know the price of a gallon of oil in pesos (for simplicity, let us avoid kilometers and liters). Describe, step-by-step, an algorithm that would compute the overall price of gasoline needed for the trip. For example, if the distance is 200 miles and your car make 25 miles per gallon, then it needs 200/25=8 gallons. At a price of 30 pesos per gallon that would mean spending 8 x 30 = 240 pesos.

1) First, divide the distance by the number of miles per gallon, producing the number of gallons. 2) Second, multiply the number of gallons by the price per gallon.3. For each of the following sequences of symbols, describe which can be valid Java identifiers and which cannot be; if you believe they cannot be, briefly explain why (e.g., "is a reserved word" or "does not start with a letter"):

- Viva Mexico
*not valid: space not allowed* - VivaMexico!
*not valid: ! not allowed* - VivaMexico
*valid* - byte
*not valid: reserved word* - byte_32
*valid*

4-5. Write a

For gas, you pay $(amount).(Do not worry about formatting.) For example, if your estimates cost is 240 pesos, the computer should print:

For gas, you pay $240.0.

*Reminder:*
to read from the screen, you can define the input object as follows:

Scanner key =the header of thenewScanner(System.in);

publicstaticvoid main(String[] args){

public static void main(String[] args){ Scanner key = new Scanner(System.in); System.out.println("Type in the distance."); double distance = key.nextDouble(); System.out.println("Type in the amount of miles per gallon."); double mpg = key.nextDouble(); double gallons = distance / mpg; System.out.println("Type in the price per gallon."); double price = key.nextDouble(); double pay = gallons * price; System.out.ptintln("For gas, you pay $" + pay + "."); }6. We hope that you did well on this test. Congratulate yourself on the job well done by writing down a line of code that, given a string

String congratulations = "Congratulations, " + yourName + ", on your first CS exam!";