Unformatted text preview: tant k
such that z = kxy .
The constant k in the above deﬁnitions is called the constant of proportionality.
4 without Calculus, that is... 4.3 Rational Inequalities and Applications 273 Example 4.3.4. Translate the following into mathematical equations using Deﬁnition 4.4.
1. Hooke’s Law: The force F exerted on a spring is directly proportional the extension x of the
2. Boyle’s Law: At a constant temperature, the pressure P of an ideal gas is inversely proportional to its volume V .
3. The volume V of a right circular cone varies jointly with the height h of the cone and the
square of the radius r of the base.
4. Ohm’s Law: The current I through a conductor between two points is directly proportional to
the voltage V between the two points and inversely proportional to the resistance R between
the two points.
5. Newton’s Law of Universal Gravitation: Suppose two objects, one of mass m and one of mass
M , are positioned so that the distance between their centers of mass is r. The...
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