Simple Clojure Exercises

Note: This is a class activity, nothing needs to be delivered.

Place all the requested functions and unit tests in a name space called simple.

Write a function called f2c that takes x degrees Fahrenheit and converts them to degrees Celsius. Unit tests:
```
(deftest test-f2c
  (is (= 100.0 (f2c 212.0)))
  (is (= 0.0 (f2c 32.0)))
  (is (= -40.0 (f2c -40.0))))
```
Tip: ºC = (ºF - 32) × 5 ÷ 9
Write a function called sign that takes an integer value n. It returns -1 if n is negative, 1 if n is positive greater than zero, or 0 if n is zero. Unit tests:
```
(deftest test-sign
  (is (= -1 (sign -5)))
  (is (= 1 (sign 10)))
  (is (= 0 (sign 0))))
```
Write a function called roots that returns a vector containing the two possible roots that solve a quadratic equation given its three coefficients (a, b, c) using the following formula:

Unit tests:
```
(deftest test-roots
  (is (= [-1 -1] (roots 2 4 2)))
  (is (= [0 0] (roots 1 0 0)))
  (is (= [-0.25 -1] (roots 4 5 1))))
```
Use the Math/sqrt function to compute the square root of a number.

The BMI (body mass index) is used to determine if a person's weight and height proportion is adequate. The BMI may be calculated using the following formula:

BMI = (weight) ÷ (height²)

Where weight should be given in kilograms and height in meters. The following table shows how different BMI ranges are classified:

BMI range	Description
BMI < 20	`underweight`
20 ≤ BMI < 25	`normal`
25 ≤ BMI < 30	`obese1`
30 ≤ BMI < 40	`obese2`
40 ≤ BMI	`obese3`

Write a function called bmi that takes two arguments: weight and height. It should return a symbol that represents the corresponding BMI description computed from its input.

Unit tests:

(deftest test-bmi
  (is (= 'underweight (bmi 45 1.7)))
  (is (= 'normal (bmi 55 1.5)))
  (is (= 'obese1 (bmi 76 1.7)))  
  (is (= 'obese2 (bmi 81 1.6)))
  (is (= 'obese3 (bmi 120 1.6))))

Programming Languages

Simple Clojure Exercises