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Direct Variation
or .
EXAMPLE 1 Solving a Direct Variation Problem
The volume of blood in a person's body varies directly as their weight . A person weighing 160 pounds has approximately 5 quarts of blood. Find for a person weighing 200 pounds.
Direct Variation with Powers
varies directly as the nth power of : or
EXAMPLE 2 Solving a Direct Variation Problem
The distance that a body falls varies directly as the square of the time of the fall. If you fall 64 feet in 2 seconds, how far will you fall in 4.5 seconds?
Inverse Variation
varies inversely as : OR .
EXAMPLE 3 Solving an Inverse Variation Problem
Pressure varies inversely as volume . If is 12 pounds per square inch in a container where is 8 cubic inches, what is the new when expands to 22 cubic inches?
EXAMPLE 4 Solving a Combined Variation Problem
Suppose that the number of sales vary directly as amount spent in advertising and inversely as price . It turns out that monthly sales are 12,000 when $60,000 is spent on advertising and price is set at $40.
4a Write an equation that describes this situation.
4b Determine sales if advertising is increased to \$70,000.
EXAMPLE 5 Modeling Joint and Combined Variation
Centrifugal force of a body moving in a circle varies jointly with the radius and the body's mass , and inversely with the square of the time it takes for one full revolution.
If a 6-gram body moving in a circle with radius 100 centimeters at a rate of 1 revolution in 2 seconds has a force of 6000 dynes, find the force of an 18-gram body moving at the rate of 1 revolution in 3 seconds.