• (3pts) 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
    The red part is called the reducible expression. You may wish to underline those in your homework by hand.

    1. (- (* 3 5) 20)
    2. (/ 44 (+ 8 3))
    3. (+ #f 10)
    4. (log (exp 1.0))
    5. (zero? (+ 2 -2))
    6. (and (= 3 3) (or (zero? 17) (> 17 0))) 
    7. (cond 
  ((zero? (sqrt 16)) #f)
  (else (+ 3 10)))

    8. (cond 
  ((and (zero? 0) (> 17 0))
   #f)
  (else 
    (+ (sin 0) 
       (* (cos 1.3) (cos 1.3)))))	   

    9. (cond 
  ((sqrt 16) #f)
  (else (+ 3 10)))
    10. Given 
      ;; experiment : number -> number 
(define (experiment t)
  (cond
    [(< t 0) 0]
    [(> (distance t) 200) 200]
    [else (distance t)]))

;; distance : number -> number 
(define (distance t)
  (* 1/2 t t G))

;; G : gravitational acceleration 
(define G 9.81)
      what are the results of 
      (experiment 5)
(experiment -1)
(experiment 20)
    Type the steps into the Definition window and check them. You may wish to use several files and print them separately.

  • (4pts) At least one of the department's professors drivers loves to accelerate quickly. He accelerates quickly when the light turns from red to green to the de-facto speed limit of 80 miles per hour (mph) and then maintains that constant speed. Write a Scheme program that takes two inputs:
    1. the acceleration (in mph per second) of a car, and
    2. an elapsed driving time in seconds
    and returns the distance traveled (in miles).

    Your physics consultant advises: Newton figured out that if an object accelerates at a (meter/second) per second [that is, "(miles per second) per second" for Libyans and Americans], it travels

    .5 * a * t * t

    meters [miles] in t seconds and reaches a speed of

    a * t

    meters per second [miles per second] in the same time span.

    Hint: Use several helper functions to make your program more readable.

  • (3pts) Either Exercise 6.3.2 or 6.3.3.

  • (Extra credit: 3pts) Exercise 6.3.4. Extend only the exercise you chose in item 3.