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The hourly temperature at Portland, Oregon, on a particular day is recorded below.
1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon
46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69°
1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight
72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°

a. Find the amplitude of a sinusoidal function that models this temperature variation

b. Find the vertical shift of a sinusoidal function that models this temperature variation.

c. What is the period of a sinusoidal function that models this temperature variation?

d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.

e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?

Respuesta :

a. Amplitude: 19.58

b. Vertical Shift is 57.42.

c. Period = 27.56146

d.  19.58 × sin(0.22797x + 1.79552) + 58.00713

e. Model's Temperature at 10 A.M.: f(-7) = 61.91

How to illustrate the information?

Amplitude is the extent or range of property, or process, such as the extent of a movement measured from the mean position to an extreme. The term sinusoidal describes a curve, referred to as a sine wave or a sinusoid, which exhibits smooth, periodic oscillation. It should be noted that sinusoidal is named based on the function y = sin(x). It occurs often in physics, engineering, etc.

The amplitude of a sinusoidal function that models this temperature variation will be:

= 77 - 1378/24

= 77 - 57.42

= 19.58

The vertical shift of a sinusoidal function that models this temperature variation us 57.42.

The period of a sinusoidal function that models this temperature variation is 27.56146.

The sinusoidal function that models this temp. variation will be

19.58 × sin(0.22797x + 1.79552) +58.00713

Learn more about amplitude on:

https://brainly.com/question/3613222

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