Beginning Algebra, 11th Edition

480 CHAPTER 7 Rational Expressions and Applications

18.Bill Veeck was the owner of several major

league baseball teams in the 1950s and 1960s.

He was known to often sit in the stands and en-

joy games with his paying customers. Here is a

quote attributed to him:

I have discovered in 20 years of moving

around a ballpark, that the knowledge of

the game is usually in inverse proportion

to the price of the seats.

Explain in your own words the meaning of his statement. (To prove his point, Veeck once

allowed the fans to vote on managerial decisions.)

Solve each problem involving direct or inverse variation. See Examples 1 and 3.

19.If xvaries directly as y, and when , find xwhen.

20.If zvaries directly as x, and when , find zwhen.

21.If dvaries directly as t, and when , find dwhen.

22.If dvaries directly as r, and when , find dwhen.

23.If xvaries inversely as y, and when , find ywhen.

24.If zvaries inversely as x, and when , find zwhen.

25.If pvaries inversely as q, and when , find pwhen.

26.If mvaries inversely as r, and when , find mwhen.

27.If mvaries inversely as , and when , find mwhen

28.If avaries inversely as , and when , find awhen.

29.If pvaries inversely as , and when , find pwhen.

30.If zvaries inversely as , and when , find zwhen.

Solve each variation problem. See Examples 1–4.

31.The interest on an investment varies directly as the rate of interest. If the interest is $48

when the interest rate is 5%, find the interest when the rate is 4.2%.

32.For a given base, the area of a triangle varies directly as its height. Find the area of a tri-

angle with a height of 6 in., if the area is 10 in.^2 when the height is 4 in.

x^2 z= 9 x=^23 x= 45

q^2 p= 4 q=^12 q= 23

b^2 a= 48 b= 4 b= 7

p^2 m= 20 p= 2 p=5.

m= 12 r= 8 r= 16

p= 7 q= 6 q= 2

z= 50 x= 2 x= 25

x= 3 y= 8 x= 4

d= 200 r= 40 r= 60

d= 150 t= 3 t= 5

z= 30 x= 8 x= 4

x= 27 y= 6 y= 2

16 in.

?

75 lb

200 lb

33.Hooke’s law for an elastic spring states

that the distance a spring stretches varies

directly with the force applied. If a force

of 75 lb stretches a certain spring 16 in.,

how much will a force of 200 lb stretch

the spring?

34.The pressure exerted by water at a given

point varies directly with the depth of

the point beneath the surface of the wa-

ter. Water exerts 4.34 lb per for

every 10 ft traveled below the water’s

surface. What is the pressure exerted on

a scuba diver at 20 ft?

in.^2

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