SOLUTION: If f(x) varies inversely as x, prove that f(x2) = f(x1)(x1/x2). Use this formula to solve the following direct variation without solving for the constant of variation.
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Question 257349: If f(x) varies inversely as x, prove that f(x2) = f(x1)(x1/x2). Use this formula to solve the following direct variation without solving for the constant of variation.
The volume of a gas varies inversely as the pressure (assuming the temperature remains constant.) An experiment shows that a particular gas has a volume of 2.4 liters under a pressure of 280 grams per square centimeter. What volume will the gas have when a pressure of 330 grams per square centimeter is applied? Answer by drk(1908) (Show Source):
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prove:
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f(x1) = k/x1
f(x2) = k/x2
f(x1)*(x1/x2) = (k/x1)*(x1/x2) = k/x2
therefore,
f(x2) = f(x1)*(x1/x2)
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We can solve the question using
V2 = P1*V1/P2
V2 = 280*2.4/330 ~ 2.03636
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