Final answer:
The amplitude of the function 3.8 cos(9πx/6) is 3.8, and the period is calculated as 4/3 by using the formula for the period of a cosine function, which is 2π/B where B is the coefficient of x within the cosine.
Step-by-step explanation:
To find the amplitude and period of the function 3.8 cos(9πx/6), we look at the standard form of a cosine function, which is A cos(Bx - C) + D, where A is the amplitude, and the period is given by 2π/B.
The amplitude of this function can be read directly from the equation, as it is the coefficient before the cosine function, which is 3.8. So, the amplitude is 3.8.
To determine the period, we take the coefficient of x within the cosine function, which is (9π/6), and set it equal to B. To find the period, we calculate 2π divided by B (9π/6), which simplifies to 2π/(9π/6) = 2π×6/9π = 12/9 = 4/3. Hence, the period is 4/3.
The correct answer is a) Amplitude: 3.8, Period: 4/3.