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Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours
since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is
10.5 meters (a minimum). The period of the function is 12.5 hours.
After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest
tenth of an hour

2.2hours
6.3hours
12.1hours
12.5hours

Respuesta :

Answer:

2.2 hours

Step-by-step explanation:

The equation to graph is

4.5cos(4pi/25 x)+15

Find amplitude by subtracting min from max and dividing it by two. a=4.5

Find vertical shift k by finding the midline. Either add 4.5 to 10.5 or subtract 4.5 from 19.5. k = 15

The period is given to be 12.5. Use formula 2pi/b = period to find b. b = 4pi/25

Put the equation into graphing calculator and find what x equals when the graph is 17 (for the first time)

Cricetus

Water expected 2.2 hours to reach a depth.

Given:

  • Maximum level = 19.5 m
  • Minimum level = 10.5 m
  • Period of function = 12.5 hours
  • Required depth = 17 m

Now,

The amplitude will be:

= [tex]\frac{Maximum - Minimum}{2}[/tex]

By substituting the values,

= [tex]\frac{19.5-10.5}{2}[/tex]

= [tex]4.5[/tex]

Equation of graph will be:

= [tex]4.5 Cos (\frac{4 \pi}{25} x)+15[/tex]

Now,

The vertical shift = [tex]10.5+4.5 = 19.5-4.5[/tex]

                                             [tex]k = 15[/tex]

 

∴ [tex]\frac{2 \pi}{b} = period[/tex]

or,

    [tex]b = \frac{2 \pi}{period}[/tex]

       [tex]= \frac{4 \pi}{25}[/tex]

With the help of graphing calculator, the graph is 17 for "x = 2.2".

Thus the answer above i.e., "option 1" is correct.

Learn more about function here:

https://brainly.com/question/19160810

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