NAME
CLASS
DATE
_
Practice
8.1
Inverse, Joint, and Combined Variation
For Exercises 1-4, y varies inversely as x. Write the appropriate
inverse-variation equation, and find y for the given values of x.
1. y
= 12 when x = 7; x = 5, 10, 16, and 20
2. Y
3. Y
1
= 3'3when
x = 45; x = 6, 15,20, and 60
4.
= 0.4 when x = 2; x = 0.1,5,8, and 20
Y = 12 when x = 0.4; x = 0.5,6,10, and 16
For Exercises 5-8, y varies jointly as x and z. Write the appropriate
joint-variation equation, and find y for the given values of x and z.
= 120 when x = 2.5 and z = 2;
x= 3andz= 2
= 16 when x = 4 and z = 0.5;
x = 2 and z = 0.25
6. Y
= 12 when x = 4 and z = 5;
x = 6 andz = 3
8. Y
5. Y
7. Y
= 192 when x = 2 and z = 3
x = 0.6 and z = 5
For Exercises 9-12, z varies jointly as x and yand inversely as w.
Write the appropriate combined-variation equation, and find z for
the given values of x, y, and w.
«
9.
co
'in
= 2.5;
10. Z
= 3.75 when x = 6,y = 12, and w = 48;
12. Z
z = 320 when x = 4,y = 10, and w
x = 5, Y = 6, and w = 8
= 3.2 when x = 0.2,y = 8, and w = 4;
x = 3, Y = 6, and w = 16
c:
~
'0
c
co
t
co
s:
Q)
c
11. Z
x = 0.05,y = 40, and w = 0.5
ii:
13.
= 4.8 when x = 0.2,y = 10, and w = 5;
1
x = 2'3' y = 5, and w = 8
The apothem of a regular polygon is the perpendicular distance from
the center of the polygon to a side. The area, A, of a regular polygon
varies jointly as the apothem, a, and the perimeter, p. A regular
triangle with an apothem of 3 inches and a perimeter of 31.2 inches
has an area of 46.8 square inches. Find the constant of variation and
write a joint-variation equation. Then find the area of a regular
triangle with an apothem of 2.3 inches and a perimeter of 12 inches.
Algebra 2
Practice Workbook
47