Beginning Algebra, 11th Edition

SECTION 7.8 Variation 479

NOW TRY
EXERCISE 4
If the area is constant, the
height of a triangle varies in-
versely as the base. If the
height is 6 ft when the base is
4 ft, find the height when the
base is 12 ft.

NOW TRY ANSWER
4.2 ft

Complete solution available
on the Video Resources on DVD

7.8 EXERCISES

Concept Check Use personal experience or intuition to determine whether the situation

suggests directorinverse variation.*

1.The number of candy bars you buy and your total price for the candy

2.The rate and the distance traveled by a moving van in 3 hr

3.The amount of pressure put on the accelerator of a truck and the speed of the truck

4.The surface area of a beach ball and its diameter

5.The number of days until the end of the baseball season and the number of home runs that

Evan Longoria has

6.“The more I see you, the more I want you.” (Opening line from a 1966 song by Chris

Montez)

7.The number of days from now until December 25 and the

magnitude of the frenzy of Christmas shopping

8.Your age and the likelihood that you believe in Santa

Claus

Concept Check Determine whether each equation represents directorinversevariation.

17.Concept Check Fill in each blank with the correct response.

(a)If the constant of variation is positive and yvaries directly as x, then as xincreases,

y.

(increases/decreases)

(b)If the constant of variation is positive and yvaries inversely as x, then as xincreases,

y.

(increases/decreases)

y=

8

x^3

y=

12

x^2

y= 50 x y= 200 x

y= y= 10 x^2 y= 3 x^3

5

x

y=

3

x

Equation for inverse variation

Substitute the given values.

Multiply by 10,000. Rewrite.

Now use

Let and

The cost per syringe to make 25,000 syringes is $0.80. NOW TRY

c= k=20,000 x=25,000.

20,000

25,000

=0.80

c=kx.

k=20,000

2 =

k

10,000

c=

k

x

*The authors thank Linda Kodama for suggesting the inclusion of exercises of this type.