Solutions — Exercises I / 2.3
  1. a.  B                   b.  B                   c.  D                  

  2. a.  B                   b.  C                   c.  C

  3. a.  A                   b.  C                   c.  D

  4. a.  Approx. 6-15 ft2  (answers may vary due to the variety of desktops)
    b.  Approx. 45-50 cm2
    c.  Approx. 90-100 in2
    d.  Approx. 100 cm2

  5. a.  360 feet                          b.  approx. 9.8 mph

  6. 90√ 2  ft  ≈  127.3 ft

  7. 22 inches

  8. a.  x = 3'  and  y = 7'
    b.  78 sq.ft.
    c.  $112.58 (for 8 2/3 sq.yd.)  or  $116.91 (for 9 sq.yd.)
    d.  $261.41 (for 8 2/3 sq.yd.)  or  $266.66 (for 9 sq.yd.)
    e.  $85.33

  9. a.  Approx. 6.4"                     b.  approx. 20"

  10. a.  Approx. 24,875 mi           b.  approx. 1036 mph

  11. Approx. 66,660 mi per hr

  12. Approx. 78,350 mph

  13. Approx. 1.5 hr = 1 hr 30 min

  14. Approx. 74 mi/hr

  15. a.  28 4/9 ft2
    b.  Approx. $19.17  (for 3.2 sq.yd.)
    c.  22-23%  and  approx. $4.33

  16. a.  Medium: approx. $0.14/in²  =  14¢/in²
    Large: approx. $0.10/in²  =  10¢/in²
    b.  Approx. $0.04/in²  =  4¢/in²

  17. 2 square pizzas:  approx. $0.066/in²  =  6.6¢/in²
    1 round pizza:  approx. $0.075/in²  =  7.5¢/in²
    ...  The two square pizza deal is slightly more economical (by almost 1¢ per sq.in.)
         than the single round large pizza.

  18. Approx. 3 times larger

  19. Approx. 260 hectares

  20. a.  Approx. 26,600 people/mi²
    b.  Approx. 6,700 people/mi²
    c.  Approx. 4 times (more crowded or dense)

  21. 21.6" × 16.2"

  22.  in ×  in  ≈  23.5" × 13.2"

  23. 316 feet

  24. a.  Approx. 74.98 miles   (Yes, virtually 75 mi... surprised?)
    b.  225 mi/hr

  25. 0.57¢/GB  or  approx. 58¢/GB (when using 1 GB = 1024 MB)

  26. a.  Approx. 0.016 MB/cm²  or  16 KB/cm²
    b.  Approx. 7.095 MB/cm2  or  7095 KB/cm²
    c.  Approx. 443 times

  27. Approx. 4.75 in

  28. Mount Everest:  approx. 0.17 mm (high)
    Mariana Trench:  approx. 0.21 mm (deep)

  29. Approx. 2.2 mm

  30. Approx. 85 ft

  31. a.  Approx. 2.9 mi                   b.  Approx. 4.3 mi

  32. Start with the Pythagorean Theorem (a² + b² = c²):
    i.e.,  d² + (3960 mi)²  =   (3960 mi + h)²
    d²  =   (3960 mi + h)² - (3960 mi)²
      =   (3960 mi)² + 2(3960 mi)h + h² - (3960 mi)²
      =   (7920 mi)h + h²
    Eventually one needs to take the positive square root of both sides of the equation in order to isolate the variable "d," however first we will tackle the discrepancy in units (since "h" is to be entered in feet whereas the radius of the Earth has already been introduced using miles)... Specifically, one needs to convert each occurence of feet into miles so that the formula indeed results in "d" being given in miles (rather than feet).
    ...   d²  =   (7920 mi)(h ft × 1 mi / 5280 ft) + (h ft × 1 mi / 5280 ft)²
      =   1.5h mi²  +  (h / 5280)² mi²
      =   [1.5h  +  h² / 27,878,400] mi² 
    And now for a novel and all-together clever observation, that is, when "h" is not very large (e.g.,
    when h < 100) then:  h² / 27,878,400 is not significant*,or its value is essentially zero...  So,
    if  h < 100,  then:   d²  ≈   [1.5h + 0] mi²
      =   1.5h mi²
    ...   d  ≈   mi
    *Try this for yourself by choosing increasingly larger numbers from 1 to 100 (and perhaps beyond) to see what decimal value results from the subsequent fractions, e.g., if h = 90 then (90)²/27,878,400  ≈  0.00029 or less than one-thousandth which is neglible when compared to 1.5h = 1.5 × 90 = 135 (and hence ultimately the difference between the square root of 135 versus the square root of 135.001 is indeed "insignificant?")