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- Multiple ChoicePlease save your changes before editing any questions.
Direct Variation
The value of y varies directly with the value of x if there exists a nonzero constant k.
FACT
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Inverse Variation
The value of y varies inversely with the value of y if there exists a nonzero constant k.
FACT
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Joint Variation
The value of y varies jointly with the value of x and z if there exists a nonzero constant k.
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Constant of Variation
It is the nonzero number k that does not change the value.
FACT
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Combined Variation
The value of y varies directly as x and jointly as z.
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On planet X, an object falls 32 feet in 2 seconds. Knowing that the distance the object will fall varies directly with the square of the time it falls, how long does it take an object to fall 200 feet?
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The amount of weight on a spring and the distance the spring will stretch is an example of Inverse Variation.
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The cost of a taxi fare (c) varies directly as the distance (d).
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The number of hours you work and the amount of paycheck is an example of Direct Variation.
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The Intensity I of light received from a source varies inversely as the square of the distance d from the source. If the light intensity is 4 feet candles at 11 feet, find the light intensity at 13 feet.
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The volume V of a cone varies jointly as its height h and the square of its radius r.
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The volume V of gas varies directly as the temperature T and inversely as the pressure P.
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The volume V of a pyramid varies jointly as its height h and the area a of its base . A pyramid with a height of 12 feet and a base with area of 23 square feet has a volume of 92 cubic feet. Find the volume of a pyramid with a height of 17 feet and a base with an area of 27 square feet.
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The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions is an example of joint variation.
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The maximum load y that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter d and inversely as the square of the height h. A 9 meter column 2 meters in diameter will support 64 metric tons. How many metric tons can be supported by a column 9 meters high and 3 meters in diameter?
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The centrifugal force C of an object moving in a circle varies jointly with the radius r of the circular path and the mass of the object m and inversely as the square of the time it takes to move about one full circle.
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The electrical resistance R of a wire varies directly as its length l and inversely as the square of its diameter d.
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The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 230 cubic centimeters when the temperature is 300ºK and the pressure is 20 pounds per square centimeter, what is the volume when the temperature is 270 ºK and the pressure is 30 pounds per square centimeter?
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Using Coulomb's Law, we know that the force exerted on each strand of hair is directly proportional to the charges on each hair and inversely proportional to the square of the distance between the two strands of hair is an example of combined variation.
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Kinetic energy KE (the energy something possesses due to being in motion) varies jointly with the mass m (in kilograms) of that object and the square of the velocity v (in meters per seconds)2 is an example of joint variation.
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