Joint and Combined Variation

Match the following. Match the items in the left column to the items in the right column. 1. joint variation 2. combined variation

1. occurs when a variable y varies directly as z 2. combines direct and inverse...

If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, find y when x is 6 and t = 3.

15

x varies directly as y, and x = 153 when y = 9. Find x when y = 13.

221

The time it takes to lay a sidewalk of a certain type varies directly as the length and inversely as the number of men working. If eight men take two days to lay 100 feet, how long will three men take to lay 150 feet?

8 days

Solve the problem as directed. The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base. If the volume of the cone is 154 cu. in. when its altitude is 12 in. and the radius of the base is 3 1/2 in., find the altitude when the volume of the cone is 77 cu. in. and the radius of the base is 2 1/3 in.

Altitude = 27/2 inches

Solve the problem as directed. The force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance d between them. Express this fact as a variation using c as a constant. Use M1 and M2 for the weights of the two bodies.

c=Fd^2/M1M2

Identify the variation as direct, inverse, joint or combined. F=kw1w2/s

combined

Identify the variation as direct, inverse, joint or combined. a1b1/c1=a2b2/c2

combined

Identify the variation as direct, inverse, joint or combined. v = cw

direct

Identify the variation as direct, inverse, joint or combined. y = cx²

direct

Identify the variation as direct, inverse, joint or combined. s/t=c

direct

Identify the variation as direct, inverse, joint or combined. s=c/t^3

inverse

Identify the variation as direct, inverse, joint or combined. l = cmn

joint

Identify the variation as direct, inverse, joint or combined.

r=cs/t