486
Chapter 9
Solving
Q
uadratic
E
quations
In Exercises 39–
4
4, write a factor that yo
u can use to
rationalize the denominator of the expression.
39.
4
—
√
—
6
40.
1
—
√
—
13
z
41.
2
—
3
√
—
x
2
42.
3
m
—
3
√
—
4
43.
√
—
2
—
√
—
5
8
44.
5
—
√
—
3
+
√
—
7
In Exercises 45–
54
, simplify the expression.
(See Example 4.)
45.
2
—
√
—
2
46.
4
—
√
—
3
47.
√
—
5
—
√
—
48
48.
—
4
—
52
49.
3
—
√
—
a
50.
1
—
√
—
2
x
5
1.
—
3
d
2
—
5
52.
√
—
8
—
√
—
3
n
3
53.
4
—
3
√
—
25
54.
3
—
1
—
108
y
2
In Exercises 55
–6
0, simplify the expression.
(See Example 5.)
55.
1
—
√
—
7
+
1
56.
2
—
5
√
—
3
57
.
√
—
10
—
7
√
—
2
58.
√
—
5
—
6
+
√
—
5
59.
3
—
√
—
5
√
—
2
60.
√
—
3
—
√
—
7
+
√
—
3
61.
MODELING WITH
MA
THEMA
TICS
The time
t
(in
seconds) it takes an object to hit the ground is gi
ven
by
t
—
h
—
16
,
where
h
is the height (in feet) from which
the object was dropped.
(
See Example 6.)
a.
How long
does it take an earring to hit the ground
when it falls from the roof of the bu
ilding?
b.
How much sooner
does the earring hit
the ground when it is
dropped from two stories
(22feet) below
the roof?
62.
MODELING WITH
MA
THEMA
TICS
The orbital period
of a planet is the time it takes the planet to tra
vel
around the Sun.
Y
ou can
nd the orbital period
P
(in Earth years) using the formula
P
√
—
d
3
,
where
d
is the av
erage distance (in astronomical units,
abbre
viated
A
U) of the planet from the Sun.
d
5.2 AU
Sun
Jupiter
a.
Simplify the formula.
b.
What is Jupiter’
s orbital period?
63.
MODELING WITH
MA
THEMA
TICS
The electric
current
I
(in amperes) an appliance uses is giv
en by
the formula
I
—
P
—
R
, where
P
is the pow
er (in watts)
and
R
is the resistance (in ohms). Find the current an
appliance uses when the pow
er is 147 watts and the
resistance is 5 ohms.
64.
MODELING WITH
MA
THEMA
TICS
Yo
u can
nd t
he
averag
e annual interest rate
r
(in decimal form) of
a savings account using the formula
r
—
V
2
—
V
0
1,
where
V
0
is the initial in
v
estment and
V
2
is the
balance of the account after 2 years. Use the formula
to compare the savings accounts. In which account
would you in
vest
money? Explain.
Account
Initial
investme
nt
Balance aft
er
2 years
1
$275
$293
2
$361
$382
3
$199
$214
4
$254
$272
5
$386
$406
55 ft
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