Question 168020: Help!
Is the equation Pressure=force/area a joint variation? How do you know?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! an excerpt from the web:
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When we say z is jointly proportional to a set of variables, it means that z is directly proportional to each variable taken one at a time.
If z varies jointly with respect to x and y, the equation will be of the form z = kxy (where k is a constant).
Equation: c = 5ab
Variable c is jointly proportional to a and b. That means c is directly proportional to both a and b.
Doubling a causes c to double. Doubling b causes c to double. Doubling both a and b causes c to quadruple.
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end of excerpt.
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based on that definition, the equation as stated would not be joint.
however, if you move the equation around, then that moved around equation could be considered joint.
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your equation p = f/a does not fit the form of a joint equation, but it can be changed to read:
f = a*p
f = a*p looks like it fits the form of a joint variation if you add a k into it (k = 1 in this case), i.e. f = k*a*p.
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why f = a*p would be considered joint, while p = f/a would not is beyond me, but that's what the definition states.
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the proportion has to be direct with each of 2 or more variables taken one at a time, as stated above.
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