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
#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.
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#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.
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#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.
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#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.
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#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.
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Written Solutions:
#1:
Solutions:
a) y = 2
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#2:
Solutions:
a) p = 8
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#3:
Solutions:
a) n = 196/405
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#4:
Solutions:
a) y = 1029/8
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#5:
Solutions:
a) The light produced 2 feet away from the source is 300 foot - candles.
