Joint Variation If a variable z varies as the product of

Chapter 2, Problem 2.1.1.176

(choose chapter or problem)

Joint Variation If a variable z varies as the product of the variables x and y, we say z varies jointly as x and y, and we write \(z=k \cdot x \cdot y\), where k is the constant of variation. Write a sentence that expresses the relationship in each of the following formulas, using the language of joint variation.

(a) \(F=m \cdot a\), where F and a are the force and acceleration acting on an object of mass m.

(b) \(K E=(1 / 2) m \cdot v^{2}\), where KE and v are the kinetic energy and velocity of an object of mass m.

(c) \(F=G \cdot m_{1} \cdot m_{2} / r^{2}\), where F is the force of gravity acting on objects of masses \(m_{1} \text { and } m_{2}\) with a distance r between their centers and G is the universal gravitational constant.