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 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 x = 3.2, find p when z = 2.2.
#3:
Instructions: Solve each inverse variation problem.
a) If n varies inversely with w^{2} 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 x^{3} 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:
Solution:
a) y = 2
Solution:
a) p = 8
Solution:
a) n = 196/405
Solution:
a) y = 1029/8
Solution:
a) The light produced 2 feet away from the source is 300 foot - candles.