NAME
DATE
6-7
PERIOD
Word Problem Practice
Rational Equations and Inequalities
4. TETHERS A tether is being attached
to a 25-foot pole in such a way that
x + y = 50. By the Pythagorean
x2 + 252 .
Theorem, the distance y = √
What must x be?
1000
2. LATERAL AREA The lateral area of a
cone with base radius r and height h is
r2 + h2 .
given by the formula L = πr √
A cone has a lateral area of 65π square
units and a base radius of 5 units.
25 ft
y
h
x
r
18.75 ft
5. RANGE NASA’s Near-Earth Asteroid
What is the height of the cone?
Tracking System tracks more than 300
asteroids. An asteroid is passing near
Earth. If Earth is located at the origin of
a coordinate plane, the path that the
asteroid will trace out is given by
17
y=−
x , x > 0. One unit corresponds to
one million miles. Carl learns that he
will be able to see the asteroid with his
telescope when the asteroid is
145
million miles of Earth.
within −
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12 units
3. ORIGAMI Georgia wants to fold a
square piece of paper into an equilateral
triangle. She wants to locate the
distance x up the side of the square
where she can make the fold indicated
by the dashed line in the figure so that
a = b. From geometry class, she knows
1 + x2 and b = √
2 (1 - x).
that a = √
So the equation she must solve is
(1 - x). What is x?
√
1 + x2 = √2
12
a. Write an expression that gives the
distance of the asteroid from Earth as
a function of x.
289
x +−
√
x
2
2
45˚
x
b. For what values of x will the asteroid
be in range of Carl’s telescope?
b
17
−
≤ x ≤ 12
12
a
1
2 - √
3
Chapter 6
49
Glencoe Algebra 2
Lesson 6-7
1. SIGNS A sign painter must spend
2
−
$8n 3 + 400 to make n signs. How many
signs can the painter make for $1200?