College Algebra 9th txtbk

64 CHAPTER 1 EQUATIONS AND INEQUALITIES
79. Replace each question mark with 6 or 7, as appropriate:
(A) If a b 1, then a ? b.
(B) If u v 2, then u ? v.
80. For what p and q is p q 6 p q?
81. If both a and b are negative numbers and ba is greater than 1,
then is a b positive or negative?
82. If both a and b are positive numbers and ba is greater than 1,
then is a b positive or negative?
83. Indicate true (T) or false (F):
(A) If p 7 q and m 7 0, then mp 6 mq.
(B) If p 6 q and m 6 0, then mp 7 mq.
(C) If p 7 0 and q 6 0, then p q 7 q.
84. Assume that m 7 n 7 0; then
But it was assumed that n 7 0. Find the error.
Prove each inequality property in Problems 85–88, given a, b, and
c are arbitrary real numbers.
85. If a 6 b, then a c 6 b c.
86. If a 6 b, then a c 6 b c.
87. (A) If a 6 b and c is positive, then ca 6 cb.
(B) If a 6 b and c is negative, then ca 7 cb.
88. (A) If a 6 b
a
and c is positive, then
c 6 b c .
a
(B) If a 6 b and c is negative, then
c 7 b c .
APPLICATIONS
mn 7 n 2
mn m 2 7 n 2 m 2
m(n m) 7 (n m)(n m)
m 7 n m
0 7 n
Write all your answers using inequality notation.
89. EARTH SCIENCE In 1970, Russian geologists began drilling a
very deep borehole in the Kola Peninsula. Their goal was to reach a
depth of 15 kilometers, but high temperatures in the borehole
forced them to stop in 1994 after reaching a depth of 12 kilometers.
They found that the approximate temperature x kilometers below
the surface of the Earth is given by
T 30 25(x 3)
3 x 12
where T is temperature in degrees Celsius. At what depth is the temperature
between 150°C and 250°C, inclusive?
90. EARTH SCIENCE As dry air moves upward it expands, and in so
doing it cools at a rate of about 5.5°F for each 1,000-foot rise up to
about 40,000 feet. If the ground temperature is 70°F, then the temperature
T at height h is given approximately by T 70 0.0055h.
For what range in altitude will the temperature be between 26°F and
40°F, inclusive?
91. BUSINESS AND ECONOMICS An electronics firm is planning
to market a new graphing calculator. The fixed costs are $650,000
and the variable costs are $47 per calculator. The wholesale price of
the calculator will be $63. For the company to make a profit, it is
clear that revenues must be greater than costs.
(A) How many calculators must be sold for the company to make a
profit?
(B) How many calculators must be sold for the company to break
even?
(C) Discuss the relationship between the results in parts A and B.
92. BUSINESS AND ECONOMICS A video game manufacturer is
planning to market a handheld version of its game machine. The
fixed costs are $550,000 and the variable costs are $120 per
machine. The wholesale price of the machine will be $140.
(A) How many game machines must be sold for the company to
make a profit?
(B) How many game machines must be sold for the company to
break even?
(C) Discuss the relationship between the results in parts A and B.
93. BUSINESS AND ECONOMICS The electronics firm in Problem
91 finds that rising prices for parts increases the variable costs to
$50.50 per calculator.
(A) Discuss possible strategies the company might use to deal with
this increase in costs.
(B) If the company continues to sell the calculators for $63, how
many must they sell now to make a profit?
(C) If the company wants to start making a profit at the same production
level as before the cost increase, how much should they increase
the wholesale price?
94. BUSINESS AND ECONOMICS The video game manufacturer in
Problem 92 finds that unexpected programming problems increases
the fixed costs to $660,000.
(A) Discuss possible strategies the company might use to deal with
this increase in costs.
(B) If the company continues to sell the game machines for $140,
how many must they sell now to make a profit?
(C) If the company wants to start making a profit at the same production
level as before the cost increase, how much should they increase
the wholesale price?
95. ENERGY If the power demands in a 110-volt electric circuit in
a home vary between 220 and 2,750 watts, what is the range of current
flowing through the circuit? (W EI, where W Power in
watts, E Pressure in volts, and I Current in amperes.)
96. PSYCHOLOGY A person’s IQ is given by the formula
IQ MA
CA 100
where MA is mental age and CA is chronological age. If
80 IQ 140
for a group of 12-year-old children, find the range of their mental
ages.