Question

HELP I HAVE A TEST TMR MORNING!!!!!!
A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8m and the cycle is repeated every 4 s.
Here is the equation that models this: $f(x)=0.9sin(\frac{\pi }{2} x)$
^The y-coordinates are in m and the x coordinates is the time in seconds

b) Use the model to determine when, during each cycle, the boat is 0.5m above the mean positition.

BRAINLIEST!!!!

Answer 1

The time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s

Since y = f(x) = 0.9sin(πx/2)

We want to determine the time, x at which the boat is 0.5 m above its mean position. This is the value of y at y = 0.5 m

So, y = f(x) = 0.9sin(πx/2)

0.5 = 0.9sin(πx/2)

Dividing through by 0.9, we have

0.5/0.9 = sin(πx/2)

5/9 = sin(πx/2)

Taking inverse sine of both sides, we have

sin⁻¹(5/9) = πx/2

sin⁻¹(0.5556) = πx/2

0.589 rad = πx/2

x = 2 × 0.589/π

x = 1.178/π

x  = 0.375 s

Since the boat repeats its cycle every 4 seconds, the time the boat is 0.5 m above the mean position after n cycles is t = (4n + 0.375) swhere n is a positive integer. That is n = 0, 1, 2, 3...

So, the time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s

Learn more about sine function here:

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