### Assignment 0: Finger Exercises -- Solutions

1. Convert each of the following expressions into Scheme:

1. 4 + 6 + 7

Solution: (+ 4 6 7) or (+ 4 (+ 6 7))

2. 5 * (5 + 9)

Solution: (* 5 (+ 5 9))

3. (4 + 9) * (8 - 7)

Solution: (* (+ 4 9) (- 8 7))

4. ((a * a) + (b * b)) / 2

Solution: (/ (+ (* a a) (* b b)) 2)

2. Convert the following function definitions into Scheme:

1. square(x) = x * x

Solution: (define (square x) (* x x))

2. avg(x, y) = (x + y) / 2

Solution: (define (avg x y) (/ (+ x y) 2))

3. celc->fahr(deg) = 9/5 * deg + 32

Solution: (define (celc->fahr deg) (+ (* (/ 9 5) deg) 32))

3. Evaluate each of the following expressions. Show every step. For example:
```  (sqrt (+ (* 3 3) (* 4 4)))
= (sqrt (+ 9 (* 4 4)))
= (sqrt (+ 9 16))
= (sqrt 25)
= 5
```

1. (- (* 3 5) 20)

Solution:

```
(- (* 3 5) 20)
= (- 15 20)
= -5
```

2. (/ 44 (+ 8 3))

Solution:

```  (/ 44 (+ 8 3))
= (/ 44 11)
= 4
```

3. (sqrt (square 6))

Solution:

```  (sqrt (square 6))
= (sqrt (* 6 6))
= (sqrt 36)
= 6
```

4. (avg 6 10)

Solution:

```  (avg 6 10)
= (/ (+ 6 10) 2)
= (/ 16 2)
= 8
```

5. (celc->fahr 100)
```  (celc->fahr 100)
= (+ (* (/ 9 5) 100) 32))
= (+ (* 9/5 100) 32)
= (+ 180 32)
= 212
```

 Kathi Fisler This page was generated on Fri Aug 27 17:01:35 CDT 1999.