Note: All of these problems are for practice. You are freely encouraged to work together and you do not need to submit any of this work for a grade.

1. Write a program that asks a user for their favorite fruit, and then prints a response as follows:

   What is your favorite fruit? apple I like apples too.

   For the sake of simplicty, assume that you may simple add an 's' to the end of the response to make it plural.

   Answer: Show/Hide

      fruit = input('What is your favorite fruit? ')
      print('I like ' + fruit + 's too.')

2. Write a program that asks the user to enter a temperature in Fahrenheit and reports the equivalent temperature in Celsius. You may use the formula $c = \frac{5}{9}(f - 32)$ for doing the conversion. A sample session might appear as follows:

   Enter a temperature in Fahrenheit: 85 85 Fahrenheit is equivalent to 29.4444 Celsius.

   Answer: Show/Hide

      fahr = float(input('Enter a temperature in Fahrenheit: '))
      celsius = 5 * (fahr - 32.0) / 9
      print(fahr, 'Fahrenheit is equivalent to', celsius, 'Celsius.')

3. Write a program that prompts the user for the radius of a circle, and which reports both the circumference and the area of that circle. As a reminder the circumference would be $2\pi r$ and the area would be $\pi r^2$. A sample session might appear as follows:

   What is the radius of your circle? 5 A circle of radius 5 has circumference 31.4159 and area 78.53975.

   Answer: Show/Hide

      r = float(input('What is the radius of your circle? '))
      circ = 3.14159 * 2 * r
      area = 3.14159 * r * r
      print('A circle of radius', r, 'has circumference', circ)
      print('and area', str(area) + '.')

4. There is a classic story (maybe it's even true) about mathematician Carl Gauss as a child. The story isthat a teacher, wanting to keep him busy for a long time, asked Gauss to compute the sumof the numbers from 1 to 100. Though the teacher presumed he would need to take time to repeatedly add one number at a time to the total, he returned quickly with the correct answer, answer, having effectively derived that the sum of the first $n$ numbers equals $\frac{n(n+1)}{2}$.

   Though we will eventually learn to use loops in Python to automate repetitive tasks, we can follow Gauss's lead for now, to compute the sum of the first $n$ number without loops. Write a program that produces an interaction as follows.

   Please enter a value for n: 100 The sum of the first 100 numbers is 5050.

   Answer: Show/Hide

      n = int(input('Please enter a value for n: '))
      total = n*(n+1) // 2                                             # integer division
      print('The sum of the first', n, 'numbers is', str(total)+'.')

5. Write a program that prompts the user for the length of the hypotenuse of a right triangle, and for the length of on of its legs, and which computes and outputs the length of the second leg. A sample session might appear as follows:

   Let's discuss a right triangle. What is the length of the hypotenuse? 5 What is the length of one of the legs? 4 The length of the other leg is 3.0.

   Answer: Show/Hide

      print("Let's discuss a right triangle.")      # doublequote as string delimeter
      c = float(input('What is the length of the hypotenuse? '))
      a = float(input('What is the length of one of the legs? '))
      b = (c**2 - a**2) ** 0.5
      print('The length of the other leg is', str(b) + '.')

6. While a person's pulse is generally reported in beats per minute, technicians rarely monitor for a full minutes, but instead extrapolate after observing a shorter time. For example, if there were 20 beats in 15 seconds, then the pulse is 80 beats per minute.

   Write a program that assists with this calculation, after receiving input about the user's observations. Presume that the pulse should be reported as a (truncated) whole number. A sample session might appear as follows:

   How many beats were observed? 20 How many seconds were observed? 18 The pulse is 66 beats per minute.

   Answer: Show/Hide

      beats = int(input('How many beats were observed? '))
      secs = int(input('How many seconds were observed? '))
      pulse = 60 * beats // secs
      print('The pulse is', pulse, 'beats per minutes')

7. Write a program that computes the roots of the classic quadratic equation, $Ax^2 + Bx + C = 0$, with the user providing the constants $A$, $B$, and $C$. You may use the quadratic formula which states that the roots are $$\frac{-B + \sqrt{B^2-4AC}}{2A}, \frac{-B - \sqrt{B^2-4AC}}{2A}$$ and you may assume, for simplicity, that the roots are well-defined (although conveniently Python has support for complex roots). A sample session might appear as follows:

   Solving quadratic equation A*x*x + B*x + C = 0. What is A? 2 What is B? -5 What is C? -3 One root is 3.0. The other is −0.5.

   Answer: Show/Hide

      print('Solving quadratic equation A*x*x + B*x + C = 0.')
      a = float(input('What is A? '))
      b = float(input('What is B? '))
      c = float(input('What is C? '))
      det = (b*b - 4*a*c)**0.5
      root1 = (-b + det)/(2*a)
      root2 = (-b - det)/(2*a)
      print('One root is', str(root1) + '.')
      print('The other is', str(root2) + '.')