Intermediate Algebra (11th edition)

SECTION 7.6 Variation 413

Concept Check Determine whether each equation represents direct, inverse, joint, or
combinedvariation.

9. 
   
   
   
   10. 
       
       
       
       11. 
           
           
           
           12. 
               
           
           
           
           
       
       
       
       
   
   
   
   

13. 14. 15. 16.

17.Concept Check For , if y varies directly as x, then when x increases, y
, and when xdecreases, y.

18.Concept Check For , if y varies inversely as x, then when x increases, y
, and when xdecreases, y.

Concept Check Write each formula using the “language” of variation. For example, the
formula for the circumference of a circle, can be written as

“The circumference of a circle varies directly as the length of its radius.”

19. where Pis the perimeter of a square with side of length s


20. where dis the diameter of a circle with radius r


21. where Sis the surface area of a sphere with radius r


22. where Vis the volume of a sphere with radius r


23. where is the area of a triangle with base band height h


24. where Vis the volume of a cone with radius rand height h

25.Concept Check What is the constant of variation in each of the variation equations in
Exercises 19 – 24?

26.What is meant by the constant of variation in a direct variation problem? If you were to
graph the linear equation for some nonnegative constant k, what role would kplay
in the graph?

Solve each problem. See Examples 1–7.

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

28.If xvaries directly as y, and when , find ywhen.

29.If avaries directly as the square of b, and when , find awhen.

30.If hvaries directly as the square of m, and when , find hwhen.

31.If zvaries inversely as w, and when , find zwhen.

32.If tvaries inversely as s, and when , find swhen.

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

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

35.pvaries jointly as qand , and when and. Find pwhen and
.

36.ƒ varies jointly as and h, and when and. Find ƒ when and
.

Solve each problem. See Examples 1–7.

37.Ben bought 15 gal of gasoline and paid $43.79. To the nearest tenth of a cent, what is the
price of gasoline per gallon?

38.Sara gives horseback rides at Shadow Mountain Ranch. A 2.5-hr ride costs $50.00. What
is the price per hour?

h= 6

g^2 ƒ= 50 g= 4 h= 2 g= 3

r= 2

r^2 p= 200 q= 2 r= 3 q= 5

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

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

t= 3 s= 5 t= 5

z= 10 w=0.5 w= 8

h= 15 m= 5 m= 7

a= 4 b= 3 b= 2

x= 10 y= 7 x= 50

x= 9 y= 3 y= 12

y=kx

V=^13 pr^2 h,

a=^12 bh, a

V=^43 pr^3 ,

S= 4 pr^2 ,

d= 2 r,

P= 4 s,

C= 2 pr,

k 70

k 70

y=

6 x

st

y=

4 x

wz

y= 3 xz^4 y= 6 x^3 z^2

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

8

x

y=

3

x