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The water level at a pier is modeled by the function y= 2.5 cos(2pi/12.5) +12, where y represents the water level measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.

ANSWER CHOICES
1.6 hours
3.1 hours
14.4 hours
19.6 hours

Respuesta :

daithiensu456

Answer: 3.1 hours

Step-by-step explanation: Just took the quiz on edg.

  Water will reach a depth of 12 meters after 3.1 hours approximately.

   Function representing the level of water by 'y' and number of hours by 'x' is,

  • [tex]y=2.5\text{cos}(\frac{2\pi x}{12.5})+12[/tex]

For y = 12 meters, (Substitute the value of y)

[tex]12=2.5\text{cos}(\frac{2\pi x}{12.5})+12[/tex]

[tex]12-12=2.5\text{cos}(\frac{2\pi x}{12.5})[/tex]

[tex]\text{cos}(\frac{2\pi x}{12.5})=0[/tex]

[tex]\frac{2\pi x}{12.5}=\frac{\pi }{2}[/tex]   (Since, [tex]\text{cos}(\frac{\pi }{2})=0[/tex])

[tex]\frac{\pi x}{12.5}=\frac{\pi }{4}[/tex]

[tex]x=\frac{\pi }{4}\times \frac{12.5}{\pi}[/tex]

[tex]x=3.125[/tex]

[tex]x\approx3.1[/tex] hours

    Therefore, water will reach a depth of 12 meters after 3.1 hours approximately.

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