Chapter 9 Radical Functions

Homework 9.3
SSM: Intermediate Algebra
73. a. ( )
( )
2 100 200
f 100 = = ≈ 2.49
32.2 32.2
It takes roughly 2.49 seconds for an object
to fall 100 feet.
b. ( )
( )
2 1483 2966
f 1483 = = ≈ 9.6
32.2 32.2
The parachutist was in freefall for roughly
9.6 seconds. This is an underestimate
because the chute would slow down his
descent.
c. f is an increasing function. This makes sense
because the higher an object is, the longer it
should take to fall to the ground.
b.
c.
d.
k
n
1/ k 1/ n
x x = x ⋅ x
3 4
= x
= x
= x
=
1 1
+
k n
n k
+
n⋅k
n⋅k
n+
k
n⋅k
n⋅ k n+
k
x
x x → k = 3, n = 4
3⋅ 4 3+
4 12 7
3 4
x x = x = x
The results are the same.
5⋅ 7 5+
7 35 12
x x = x = x
5 7
75.
3
1/ 2
1 1 3 2 1
− −
2 3 6 6 6 6
x x x x
x x
= = = = =
1/ 3
x x
77. Begin by letting the two expressions be denoted
by W and Y. We know the following from the
problem statement:
79. a.
W + Y = 9 x + 7
W − Y = x + 3
Adding the two equations together will eliminate
the Y terms and yield:
2W = 9 x + 7 + x + 3
2W
= 10 x + 10
W = 5 x + 5
Plug this into one of the original equations:
5 x + 5 + Y = 9 x + 7
Y = 9 x + 7 − 5 x − 5
Y = 4 x + 2
Thus, the two expressions are 5 x + 5 and
4 x + 2 .
3 4
1/ 3 1/ 4
x x = x ⋅ x
= x
= x
= x
=
1 1
+
3 4
4 3
+
12 12
7 /12
12 7
x
81. Answers will vary. See Key Points.
Homework 9.3
1.
3.
5.
2 2 3
= ⋅
3 3 3
=
=
2 3
( 3) 2
2 3
3
8 8 x
= ⋅
x x x
=
8
x
( x ) 2
8 x
=
x
3 3 5x
= ⋅
5x 5x 5x
=
3 5x
( 5x
) 2
3 5x
=
5x
280