Question

A gear on a machine turns at a rate of 2 revolutions per second. Let x represent time in seconds and let y represent the number of revolutions What is the equation that models the number of revolutions over time?

Answer 1

The equation modeling the number of revolutions of a gear over time, where the gear turns at 2 revolutions per second, is 'y = 2x'.

Step-by-step explanation:

To model the number of revolutions (y) of a gear over time (x) when the gear turns at a rate of 2 revolutions per second, we can use a simple linear equation. Since each second corresponds to 2 revolutions, the relationship between time and revolutions is directly proportional.

The equation that represents this linear relationship is given by:

y = 2x

This indicates that for every second that passes (x), the gear completes 2 more revolutions (y). It's important to note that we do not need to convert revolutions to radians in this context, as the question asks for the number of revolutions, not an angular displacement in radians.