g(t)=4\\sin(\\frac{\\pi t}{6}) + 5\nthe height of the average wave, in feet, over t hours, at windy beach is…

g(t)=4\\sin(\\frac{\\pi t}{6}) + 5\nthe height of the average wave, in feet, over t hours, at windy beach is modeled by function h, shown on this graph.\nthe waves at which beach take a longer period of time to complete one full wave cycle?\na. windy beach\nb. sandy beach\nc. at both beaches it takes the same amount of time to go through one full wave cycle.\nd. this cannot be determined from the given information.

g(t)=4\\sin(\\frac{\\pi t}{6}) + 5\nthe height of the average wave, in feet, over t hours, at windy beach is modeled by function h, shown on this graph.\nthe waves at which beach take a longer period of time to complete one full wave cycle?\na. windy beach\nb. sandy beach\nc. at both beaches it takes the same amount of time to go through one full wave cycle.\nd. this cannot be determined from the given information.

Answer

Answer:

A. Windy Beach

Explanation:

Step1: Find period of (g(t))

For (y = A\sin(Bt)+C), period (T=\frac{2\pi}{B}). Here (B = \frac{\pi}{6}), so (T_{g}=\frac{2\pi}{\frac{\pi}{6}}= 12) hours.

Step2: Find period of (h(t)) from graph

From the graph of (h(t)), one - full wave cycle occurs from (t = 0) to (t = 6), so (T_{h}=6) hours.

Step3: Compare periods

Since (T_{g}=12) hours and (T_{h}=6) hours, the waves at Windy Beach ((g(t))) take a longer period of time to complete one full wave cycle.