a certain radio wave travels in a path represented by the equation y = 5sin2x. what is the period of this…

Explanation:

Step1: Recall period formula for sine function

The general form of a sine - function is $y = A\sin(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$. For the function $y = 5\sin(2x)$, $B = 2$.

Step2: Calculate the period

$T=\frac{2\pi}{|2|}=\pi$

Step3: Recall amplitude formula for sine - like function

The amplitude of a function of the form $y = A\sin(Bx - C)+D$ is $|A|$. For a graph, the amplitude is half of the vertical distance between the maximum and minimum values. From the graph, the maximum value of the function is $y = 6$ and the minimum value is $y = 2$. The vertical distance between the maximum and minimum is $6 - 2=4$.

Step4: Calculate the amplitude

The amplitude $A=\frac{6 - 2}{2}=2$

Answer:

Question 1: C. $\pi$ Question 16: B. $2$