Final answer:
The total distance traveled by a pendulum that loses 6 inches on each return swing is represented by the equation d = 150 - (6n), where 'd' is the total distance and 'n' is the number of oscillations. Thus, option (a) is the correct equation for this scenario.
Step-by-step explanation:
The question involves finding an equation that represents the total distance a weight travels on a pendulum before coming to rest. On the first swing, the pendulum travels 150 inches and on the return swing, it travels 144 inches, meaning that with each complete oscillation there is a 6-inch decrement in the total distance traveled. The distance decreases linearly with each oscillation by this increment of 6 inches.
To find the total distance traveled after 'n' oscillations, we start with the initial distance of 150 inches and subtract 6 inches for each oscillation. Therefore, the equation for the total distance 'd' after 'n' oscillations is given by:
d = 150 - (6n).
This linear relationship effectively captures the cumulative effect of the distance decrement over each oscillation until the pendulum comes to rest. Hence, the correct option is a. d = 150 - (6n).