Final answer:
The constant of proportionality is denoted by the letter c, pivotal in converting proportional relationships into linear equations, such as F= m x a in Newton's second law. Constants like the speed of light (c), gravitational constant (G), and Planck's constant (h) act as constants of proportionality in physical laws. In everyday situations involving direct proportionality, such as pay per activity, it simplifies the representation of the relationship between variables.
Step-by-step explanation:
The constant of proportionality in mathematical equations is commonly represented by the letter c. This constant is essential in equations that establish a relationship where one variable is directly proportional to another. For example, in Newton's second law of motion, the force (F) is directly proportional to the product of an object's mass (m) and acceleration (a), with the proportional constant being the newton (N), which is the unit of force. Therefore, the constant of proportionality allows us to express proportional relationships as equalities, such as F= m x a.
In the field of physics, constants like the speed of light (c), gravitational constant (G), Planck's constant (h), and others, all serve as constants of proportionality in their respective formulas, providing the crucial link between variables. For instance, the Stefan-Boltzmann constant combines Planck's constant, the speed of light, and the Boltzmann constant to describe the power radiated from a black body in terms of its temperature. Similarly, Coulomb's law has the constant of proportionality known as Coulomb's constant (k), which is essential when calculating the electrostatic force between charged particles.
In simpler instances like calculating pay based on the number of calls made, as with the hypothetical college job calling alumni, the pay (p) is directly proportional to the number of calls (n), and the constant of proportionality would be the pay rate per call. This transforms a proportional relationship into a linear equation, such as p = $2.50 x n, with $2.50 being the constant of proportionality. In every case, the constant simplifies the communication of relationships between variables and is a cornerstone for problem-solving in mathematics and science.