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64.
HANG TIME
Refer to the information at the beginning of the lesson regarding hang
time. Describe how the height of a jump is related to the amount of time in the air.
Write a step-by-step explanation of how to determine the height of the volleyball
player’s 0.98-second jump.
CONCERTS
The organizers of a concert are preparing for the arrival of 50,000 people in
the open field where the concert will take place. Each person is allotted 5 square feet
of space, so the organizers rope off a circular area of 250,000 square feet. Using the
formula
A
= π
r
2
, where
A
represents the area of the circular region and
r
represents
the radius of the region, find the radius of this region.
66.
WEIGHTLIFTING
The formula
M
=
512
-
146,230
B
-
8
_
5
can be used to estimate the
maximum total mass that a weightlifter of mass
B
kilograms can lift using the snatch
and the clean and jerk. According to the formula, how much does a person weigh who
can lift at most 470 kilograms?
H.O.T. Problems
Use
H
igher-
O
rder
T
hinking Skills
67.
ERROR ANALYSIS
Which equation does not have a solution?
√
x
-
1
+
3
=
4
√
x
+
1
+
3
=
4
√
x
-
2
+
7
=
10
√
x
+
2
-
7
= -
10
68.
CHALLENGE
Lola is working to solve (
x
+
5)
1
_
4
= -
4. She said that she could tell there
was no real solution without even working the problem. Is Lola correct? Explain your
reasoning.
69.
REASONING
Determine whether
√
(
x
2
)
2
_
-
x
=
x
is
sometimes
,
always
, or
never
true when
x
is a real number. Explain your reasoning.
70.
OPEN-ENDED
Select a whole number. Now work backward to write two radical
equations that have that whole number as solutions. Write one square root equation
and one cube root equation. You may need to experiment until you find a whole
number you can easily use.
71.
WRITING INMATH
Explain the relationship between the index of the root of a variable
in an equation and the power to which you raise each side of the equation to solve the
equation.
72.
OPEN-ENDED
Write an equation that can be solved by raising each side of the equation
to the given power.
a.
3
_
2
power
b.
5
_
4
power
c.
7
_
8
power
73.
CHALLENGE
Solve 7
3
x
-
1
=
49
x
+
1
for
x
. (
Hint:
b
x
=
b
y
if and only if
x
=
y
.)
REASONING
Determine whether the following statements are
sometimes
,
always
,
or
never
true for
x
1
_
n
=
a
.
Explain your reasoning.
74.
If
n
is odd, there will be extraneous solutions.
75.
If
n
is even, there will be extraneous solutions.
65
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