Answer:
π / 15 seconds
Step-by-step explanation:
To determine the period of the function d(t) = 2sin(30t) + 5, we need to understand the general form of a sine function. The general form of a sine function is:.
y = A sin(Bx - C) + D.
In this case, the function given is d(t) = 2sin(30t) + 5. Comparing it to the general form, we can see that:.
A = 2 (amplitude).
B = 30 (frequency).
C = 0 (phase shift).
D = 5 (vertical shift).
The period of a sine function is calculated as:.
Period = 2π / |B|.
In this case, the period of the function d(t) = 2sin(30t) + 5 is:.
Period = 2π / |30| = π / 15.
Therefore, the period of the function is π / 15 seconds. This represents the time it takes for the depth of the propeller to complete one full cycle of oscillation, from its highest point to its lowest point and back to the highest point again.
