### About Inverse Variation:

After learning about rational expressions, we generally discuss direct variation and inverse variation. Inverse variation: y varies inversely with x, if there is a constant k, such that y = k/x. The problems we see in this section are very similar to our last section on direct variation.

Test Objectives
• Demonstrate the ability to find the value for the constant of variation (k)
• Demonstrate the ability to solve an inverse variation problem
• Demonstrate the ability to solve an inverse variation as a power problem
Inverse Variation Practice Test:

#1:

Instructions: Solve each inverse variation problem.

a) If y varies inversely with x and y = 10 when x = 3, find y when x = 15.

#2:

Instructions: Solve each inverse variation problem.

a) If p varies inversely with z and p = 5.5 when z = 3.2, find p when z = 2.2.

#3:

Instructions: Solve each inverse variation problem.

a) If n varies inversely with w2 and n = 4/5 when w = 7/15, find n when w = 3/5.

#4:

Instructions: Solve each inverse variation problem.

a) If y varies inversely with x3 and y = 3 when x = 7, find y when x = 2.

#5:

Instructions: Solve each inverse variation problem.

a) The amount of light measured in foot - candles varies inversely with the square of the distance from the source. If the amount of light produced 40 feet form a light source is 0.75 foot - candles, find the light produced 2 feet away from that light source.

Written Solutions:

#1:

Solutions:

a) y = 2

#2:

Solutions:

a) p = 8

#3:

Solutions:

a) n = 196/405

#4:

Solutions:

a) y = 1029/8

#5:

Solutions:

a) The light produced 2 feet away from the source is 300 foot - candles.