what is the horizontal distance between two consecutive maximums on the graph of y (3) 3 (4) 10 1 2 3 4

what is the horizontal distance between two consecutive maximums on the graph of y (3) 3 (4) 10 1 2 3 4

what is the horizontal distance between two consecutive maximums on the graph of y (3) 3 (4) 10 1 2 3 4

Answer

  1. Recall the period - formula for the sine function (y = A\sin(Bx - C)+D):
    • The general form of a sine - type function is (y = A\sin(Bx - C)+D), and its period (T=\frac{2\pi}{|B|}). The horizontal distance between two consecutive maximums (or minimums) of a sine or cosine function is equal to its period.
    • Although the function in the problem is not fully shown, assuming the function is of the form (y=\sin(\frac{\pi}{5}x)) (since the denominator of the coefficient of (x) is (5) in the visible part), here (B = \frac{\pi}{5}).
  2. Calculate the period:
    • Using the period formula (T=\frac{2\pi}{|B|}), substitute (B=\frac{\pi}{5}) into it.
    • (T=\frac{2\pi}{\frac{\pi}{5}}).
    • When dividing by a fraction, we multiply by its reciprocal, so (T = 2\pi\times\frac{5}{\pi}).
    • The (\pi) terms cancel out, and (2\times5=10).

Answer:

(4) 10