Question

Jami is modeling the movement of a tire. Which function best models the position of the nozzle?

a) s(t) = 9cos(pie/4 t)
b) s(t) = 9sin(4 pie t)
c) s(t) = 9sin(pie/4 t)
d) s(t) = 9cos(4 pie t)

Answer 1

The function that best models the position of the nozzle is
`\(s(t) = 9\sin\left((\pi)/(4)t\right)\)` thus option C is correct.

Step-by-step explanation:

In modeling the movement of a tire, the function for position
`(\(s(t)\))` should exhibit a sinusoidal behavior since tires often undergo periodic motion. Among the given options,
`\(s(t) = 9\sin\left((\pi)/(4)t\right)\)` represents the most suitable model.

The sine function captures the periodic nature of the tire's movement, and the coefficient
`\((\pi)/(4)\)` in the argument influences the frequency of oscillation. The amplitude of 9 indicates the maximum displacement from the equilibrium position.

Options (a), (b), and (d) involve variations in the trigonometric functions or different frequencies, which may not accurately represent the expected tire movement. Therefore, option (c) is the most appropriate choice for modeling the position of the nozzle in the context of tire motion.

In summary,
`\(s(t) = 9\sin\left((\pi)/(4)t\right)\)` best captures the sinusoidal movement associated with a tire's motion, making it the preferred function for modeling the position of the nozzle.