10.009 Week 2 Solution

• Problems: Homework: Same as for the cohort session problems.
• Problems: Exercises: These are practice problems and will not be graded. You are encouraged to solve these to enhance your programming skills. Being able to solve these problems will likely help you prepare for the midterm examination.
Objectives:
1. Learn to write and use functions.
2. Learn basic techniques for program debugging.
3. Learn to input data from the keyboard and handle user input.
4. Learn to use if-elif-else statement.
Problems: Cohort sessions
1. Functions: multivalued: Recall the following equation that gives the height of a ball at time t when it is thrown with an initial velocity of v0.

Write a function named position_velocity() that takes v0 and t as inputs and returns y(t) and y0(t), where y0(t) is the first derivative of y(t) with respect to t. Use your knowledge of calculus to find the formula to calculate y0(t). Define the gravitational constant g in your code. Round the output to two decimal places using round(n,d).
Use g = 9.81 m s−2.
>>>print(position_velocity(5.0, 10.0))
(-440.5, -93.1)
>>>print(position_velocity(5.0, 0.0)) (0.0, 5.0)
>>>print(position_velocity(0.0, 5.0))
(-122.62, -49.05)
2. Functions: BMI: Write a function that takes in your weight in kilograms and your height in centimetres, and returns your Body Mass Index (BMI). The BMI can be calculated by taking the weight in kilograms and dividing it by the square of your height in meters. You can assume that the height is never zero. Note that one meter is one hundred centimeter.
Round the output to one decimal place using round() function. For example:
>>>print(bmi(60,120)) 41.7
>>>print(bmi(50,150))
22.2
>>>print(bmi(43.5,142.3))
21.5
Write a test program that prompts the user to enter the weight and height as follows.
Weight in kilograms: 95.5
Height in centimetres: 180
BMI: 29.5
Vocareum Submission: Submit only the function definition without the test program.
3. Functions: Area of a Triangle: Write a function that takes in the three points (x1,y1),
(x2,y2), and (x3,y3) of a triangle and returns its area. The formula for computing the area
of a triangle is

where siden is the length of one of the sides of a triangle. The three points are of the type
Coordinate defined as:
class Coordinate: x = 0.0 y = 0.0
See the figure below. Round your answer to two decimal places. To test the function,

you can use the following code:
print("Test Case 1") p1=Coordinate() p1.x=1.5 p1.y=-3.4 p2=Coordinate() p2.x=4.6 p2.y=5 p3=Coordinate() p3.x=9.5 p3.y=-3.4
ans=area_of_triangle(p1,p2,p3) print(ans)
print("Test Case 2") p1=Coordinate() p1.x=2.0 p1.y=-3.4 p2=Coordinate() p2.x=4.6 p2.y=5 p3=Coordinate() p3.x=9.5 p3.y=-1.4
ans=area_of_triangle(p1,p2,p3) print(ans) print("Test Case 3") p1=Coordinate() p1.x=1.5 p1.y=3.4 p2=Coordinate() p2.x=4.6 p2.y=5 p3=Coordinate() p3.x=-1.5
p3.y=3.4
ans=area_of_triangle(p1,p2,p3) print(ans)
print("Test Case 4") p1=Coordinate() p1.x=-1.5
p1.y=3.4 p2=Coordinate() p2.x=4.6 p2.y=5 p3=Coordinate() p3.x=4.3 p3.y=-3.4
ans=area_of_triangle(p1,p2,p3) print(ans)
The expected output should be:
Test Case 1:
33.6
Test Case 2:
28.9
Test Case 3:
2.4
Test Case 4:
25.38
Write a test program that prompts the user to enter the coordinates of the three sides and display the area. Here is a sample run:
Enter x coordinate of the first point of a triangle: 1.5
Enter y coordinate of the first point of a triangle: -3.4
Enter x coordinate of the second point of a triangle: 4.6
Enter y coordinate of the second point of a triangle: 5
Enter x coordinate of the third point of a triangle: 9.5
Enter y coordinate of the third point of a triangle: -3.4
The area of the triangle is 33.6
Vocareum Submission: Submit only the function definition without the test program.
4. Program tracing: What is printed when the following Python code snippets are executed?
For each problem assume three cases: Case 1: x < y, Case 2: x > y, and Case 3: x = y.
Note: Submit the answer on eDimension.
(a) if x<y: print(x)
elif x>y:
print(y)
else: print(x+y) (b) if x<y: print(x+y)
elif x>y: print(y) if x==y: print(x-y)
else: print(x)
5. Functions and conditions: Write a function called describe_bmi that takes in a BMI value, and returns a string. The output string should follow the conditions specified by the Healthhub.sg (https://www.healthhub.sg/live-healthy/410/Healthy%20Weight).
• bmi < 18.5: nutritional deficiency
• 18.5 <= bmi < 23: low risk
• 23 <= bmi < 27.5: moderate risk
• 27.5 <= bmi: high risk
An example of test cases are:
>>> describe_bmi(18) nutritional deficiency >>> describe_bmi(18.5) low risk
>>> describe_bmi(20) low risk
>>> describe_bmi(23) moderate risk >>> describe_bmi(27.5) high risk >>> describe_bmi(30) high risk
6. Functions and conditions: Write a function named letter_grade that takes an integer argument, which represents a mark of a student. Return ‘A’ if mark ≥ 90, ‘B’ if 80 ≤ mark < 90, ‘C’ if 70 ≤ mark < 80, ‘D’ if 60 ≤ mark < 70, and ‘E’ if mark < 60. Return
None if it is not a valid mark. A valid mark ranges from 0 to 100.
>>>print(letter_grade(102)) None
>>>print(letter_grade(100)) A
>>>print(letter_grade(83)) B
>>>print(letter_grade(75)) C
>>>print(letter_grade(67)) D
>>>print(letter_grade(52)) E
>>>print(letter_grade(-2)) None
7. Functions and Conditionals: Two Squares: Write a function called is_in_square() that takes in two Coordinate objects and two floats that represent two squares. Each square is represented by a Coordinate that specifies its centre as well as a float that specifies its side. If the second square is within the first square, or overlaps the first square, the function should return True, otherwise it should return False. The diagram shows all the cases where the function should return True. In the case on the right, it is True because the edges of the two squares overlap.

Design your own test cases and verify the function. An example would be:
>>> s1 = Coordinate()
>>> s1.x, s1.y = 10, 10 >>> s2 = Coordinate()
>>> s2.x, s2.y = 20, 10
>>> is_in_square(s1, 5, s2, 4) False
Problems: Homework
1. Functions: Temperature conversion: Write a function named fahrenheit_to_celsius. This function takes a fahrenheit value as input and returns its centigrade equivalent. Recall: If C denotes the centigrade value and F its fahrenheit equivalent, then F =
C ∗ 9/5 + 32. For example:
>>>print(fahrenheit_to_celsius(32))
0.0
>>>print(fahrenheit_to_celsius(-40)) -40.0
>>>print(fahrenheit_to_celsius(212))
100.0
2. Functions: Temperature conversion: Write a function named celsius_to_fahrenheit that returns the fahrenheit equivalent of a centigrade value input as an argument.
>>>print(celsius_to_fahrenheit(0))
32.0
>>>print(celsius_to_fahrenheit(-40)) -40.0
>>>print(celsius_to_fahrenheit(100))
212.0
3. Functions: Volume of a cylinder Write a function that takes in the radius and the length of a cylinder and returns the area and volume using the following formulas:
area = radius ∗ radius ∗ π volume = area ∗ length
Round your answer to two decimal place and output both the area and volume as a tuple.
For example,
>>>print(area_vol_cylinder(1.0,2.0)) (3.14, 6.28)
>>>print(area_vol_cylinder(2.0,2.3))
(12.57, 28.9)
>>>print(area_vol_cylinder(1.5,4))
(7.07, 28.27)
>>>print(area_vol_cylinder(2.2,5.0))
(15.21, 76.03)
4. Functions: Wind-chill temperature How cold is it outside? The temperature alone is not enough to provide the answer. Other factors such as wind speed, relative humidity, and sunshine play important roles in determining coldness outside. In 2001, the National Weather Service (NWS) implemented the new wind-chill temperature to measure the coldness using temperature and wind speed.
twc = 35.74 + 0.6215ta − 35.75v0.16 + 0.4275tav0.16
Write a function that takes in a temperature and a wind speed and returns the wind-chill temperature.
>>>print(wind_chill_temp(5.3,6)) -5.56706845588
>>>print(wind_chill_temp(2.2,4))
-6.34646224199
Write a test program that prompt the user to key in the temperature and the wind speed
as follows.
Outside temperature in Fahrenheit: 5.3 Wind speed in miles per hour: 6 wind chill index: -5.56707
Vocareum Submission: Submit only the function definition without the test program.
5. Functions: Number of years and days: Write a function minutes_to_years_days that takes in minutes as its input parameter, and returns the number of years and days for the minutes. For example, if the function takes in 527040 minutes, it is equivalent to 366 days, and so it will return 1 year and 1 day. For simplicity, assume a year has 365 days and round down the remaining days. For example,
>>>print(minutes_to_years_days(1000000000)) (1902, 214)
>>>print(minutes_to_years_days(2000000000))
(3805, 63)
Test the function by writing a test program that prompts the user, using input, to enter the minutes and print the output of the function. Here is a sample run:
Enter the number of minutes: 1000000000
1000000000 minutes is approximately 1902 years and 214 days.
6. Functions: Future investment value: Write a function that takes in an investment amount, the annual interest rate in percentage term, and the number of years, and returns the future investment value using the following formula:
futureInvestmentV alue = investmentAmount×(1+monthlyInterestRate)numberOfMonths
For example:
>>>print(investment_val(1000,4.25,1)) 1043.34
>>>print(investment_val(1500,3.25,2))
1600.6
>>>print(investment_val(1000,2.25,0.5))
1011.3
>>>print(investment_val(2000,4.25,3))
2271.46
Round the answer to two decimal places.
Write a test program that keys in the investment amount, annual interest rate, and the number of years. Here is a sample run:
Enter investment amount: 1000
Enter annual interest rate (%): 4.25
Enter number of years: 1
Accumulated value is 1043.33
Vocareum Submission: Submit only the function definition without the test program.
7. Functions: largest number: Write a function named is_larger that takes two numbers, say n1 and n2, as inputs. If n1 > n2 the function returns True otherwise it returns False. You can assume that the inputs are always numbers, i.e. either integers or floats.
>>>print(is_larger(2,-1)) True
>>>print(is_larger(-1,2))
False
>>>print(is_larger(2,2)) False
8. Functions: Arguments: Write a function named check_value that takes four integers n1, n2, n3, and x as inputs. The function returns True if x is greater than n1 and n2 but is less than n3, otherwise it returns False.
print("Test case 1: check_value(1,4,8,7)") print("ans = True") ans=check_value(1,4,8,7)
print(ans)
print("Test case 2: check_value(10,4,8,7)") print("ans = False") ans=check_value(10,4,8,7) print(ans)
print("Test case 3: check_value(1,10,8,7)") print("ans = False") ans=check_value(1,10,8,7) print(ans)
print("Test case 4: check_value(1,4,5,7)") print("ans = False") ans=check_value(1,4,5,7) print(ans)
The output should be:
Test case 1: check_value(1,4,8,7) ans = True
True
Test case 2: check_value(10,4,8,7) ans = False
False
Test case 3: check_value(1,10,8,7) ans = False
False
Test case 4: check_value(1,4,5,7) ans = False
False End of Problem Set 2.