602 Worked-Out Solutions to Exercises: Chapters 1 to 9
Chapter 6
- The ratio of the top wind speed in a “category 1” hurricane to the top wind speed in a
“category 4” hurricane is 95:155. It’s easy to see that both of these integers are divisible
by 5, because they both end in 5. When you divide both the numerator and the
denominator by 5, you get 19:31. These integers are both prime, so this expression of
the ratio is in lowest terms. The ratio of the top wind speed in a “category 4” hurricane
to the top wind speed in a “category 1” hurricane is found by switching the numerator
and denominator, getting 31:19. - The ratio of the absolute temperature of the boiling point to the absolute temperature
of the freezing point, expressed in kelvins, is 373:273. To get this in lowest terms,
you must find an integer that “divides out” from both of these numbers until the
denominator becomes prime. That’s not as obvious here as in Prob. 1! Start by trying to
factor 373 into a product of primes. The square root of 373 is equal to 19 followed by
Table A-6. Solution to Prob. 9 in Chap. 5. As you read down the left-
hand column, each statement is equal to every statement above it.
Statements Reasons
−(d+g) Begin here
(d+g)(−1) Principle of the sign-changing element
(−1)(d+g) Commutative law for multiplication
(−1)d+ (−1)g Distributive law for multiplication over addition
−d+ (−g) Principle of the sign-changing element (the other
way around)
−d−g Addition of a negative is the same thing as
subtraction
Q.E.D. Mission accomplishedTable A-7. Solution to Prob. 10 in Chap. 5. As you read down the
left-hand column, each statement is equal to every statement above it.
Statements Reasons
−(h−k) Begin here
(h−k)(−1) Principle of the sign-changing element
h(−1)−k(−1) Right-hand distributive law for multiplication
over subtraction
−h− (−k) Principle of the sign-changing element (the other
way around)
−h+k Subtraction of a negative is the same thing as
addition of a positive
k+ (−h) Commutative law for addition
k−h Addition of a negative is the same thing as
subtraction of a positive
Q.E.D. Mission accomplished