;tbsp->cup : Number -> Number
(define (tbsp->cup tbsps)
  (/ tbsps 16))
 
(tbsp->cup 0) 
"should be" 0
(tbsp->cup 16) 
"should be" 1
 
;cup->gal : Number -> Number
(define (cup->gal cups)
  (/ cups 16))
 
(cup->gal 0) 
"should be" 0
(cup->gal 16) 
"should be" 1
 
 
;gal->barrel: Number -> Number
(define (gal->barrel gals)
  (/ gals 42))
 
(gal->barrel 0) 
"should be" 0
(gal->barrel 42) 
"should be" 1
 
;tbsp->barrels : Number -> Number
(define (tbsp->barrels tbsps)
  (gal->barrel (cup->gal (tbsp->cup tbsps))))
 
(tbsp->barrels 0) 
"should be" 0
(tbsp->barrels 10752) 
"should be" 1
 

;volume : Number -> Number
; return the volume of a sphere given its radius
(define (volume r)
  (/ (* 4 pi (expt r 3)) 3))
 
(volume 0)
"should be" 0
(volume 1)
"should be" (* 4/3 pi)
(volume 2)
"should be" (* 4/3 pi 8)
 
;shell-volume: Number Number -> Number
(define (shell-volume r1 r2)
  (- (volume r2) (volume r1)))
 
(shell-volume 0 0)
"should be" 0
(shell-volume 0 1)
"should be" (* 4/3 pi)
(shell-volume 1 2)
"should be" (* 4/3 pi 7)
 

;fed1: Number -> Number
; given an income of $35,000 or below, return tax
(define (fed1 inc)
  (* inc .15))
 
;fed2: Number -> Number
; given an income between $35,000 and $100,000 return tax,
; only for portion greater than $35,000
(define (fed2 inc)
  (* (- inc 35000) .25))
 
 
;fed3: Number -> Number
; given an income over $100,000 return tax, only for portion
; greater than $100,000
(define (fed3 inc)
  (* (- inc 100000) .35))
 
;state1: Number -> Number
; given an income between 0 and $50,000 return 0
(define (state1 inc)
  0)
 
;state2: Number -> Number
; given an income over $50,000, return state tax amount
(define (state2 inc)
  (* (- inc 50000) .05))
 
(define (tax-for-over-100000 inc)
  (+ (fed1 35000)
     (fed2 100000)
     (fed3 inc)
     (state1 50000)
     (state2 inc)))
 
(tax-for-over-100000 100001)
"should be" (+ (* .15 35000) (* .25 65000) (* .35 1) (* .05 50001))
(tax-for-over-100000 200000)
"should be" (+ (* .15 35000) (* .25 65000) (* .35 100000) (* .05 150000))
 
;What must change?
; - only the multiplier in the state2 function
 

;; collision-speed : Num Num Num Num -> Num
(define (collision-speed m1 v1 m2 v2)
  (/ (+ (momentum m1 v1) (momentum m2 v2))
     (+ m1 m2)))
 
;; momentum : Num Num -> Num 
;; to compute the momentum from the veolicity and mass of an object
(define (momentum m v)
  (* m v))
 
(momentum 10 -3)
"should be" -30
(collision-speed 10 3 10 -3)
"should be" 0
(collision-speed 10 4 5 -20)
"should be" -4
 

  (* 0.08 30 principal))
 
(define (compute-principal sell down)
  (- sell down))
 
(define (total-cost sell down)
  (+ sell (compute-interest (compute-principal sell down)) 1000))
 
(compute-principal 100000 10000)
"should be" 90000
(compute-interest 100000)
"should be" 240000
(total-cost 110000 10000)
"should be" 351000