7th Grade Math

MUSIC The table shows the relationship between the frequency

and wavelength of a musical tone. Determine if the relationship

is an inverse variation. Justify your response.

Graph the data in Frequency (vibrations

per second)^220440660880

Wavelength (feet) 4 2 1 _^13  1

the table.

Wavelength (ft)

Frequency (vibrations per second)

Music

2

1

0

3

4

5

(^4080120160200240280320360400440480520560600640680720760800840880920)
x
y
(220, 4)
(660, 1.33)
(440, 2)
(880, 1)
The graph shows that this is an inverse variation. The x- and
y-coordinates each have a product of 880.
CONSTRUCTION The number of carpenters needed to frame a
house varies inversely as the number of days needed to complete
the project. Suppose 5 carpenters can frame a certain house in
16 days. How many days will it take 8 carpenters to frame the
house? Assume that they all work at the same rate.
Solve the problem by using inverse variation. Let x be the number
of carpenters. Let y be the number of days.
Step 1 Find the value of k.
xy = k Inverse variation
(5)(16) = k Replace y with 16.x with 5 and
80 = k Simplify to determine k.
Step 2 Find the number of days.
y = kx Definition of inverse variation
y = ^808 Replace x with 8.k with 80 and
y = 10 Simplify.
A crew of 8 carpenters can frame the house in 10 days.
a. CANDLES Graph the data Candle’s Volume
Burn Time (h) 1248
Volume (in^3 ) 128 64 32 16
in the table. Then determine
if the relationship is an
inverse variation.
Lesson 3E Variation 413
Real-World Link
Singers and musicians
use the word pitch
when referring to
frequency. They often
refer to frequencies by
using note names,
such as middle C.
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404_415_C07_L3_895130.indd 413 12/31/09 4:33 PM