I NEED HELP. PLEASE, THANKS! :)
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?

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Respuesta :

tramserran tramserran · Answer 1 · 2020-07-06T01:13:45+02:00

Answer: (a) Amplitude = 19

(b) Vertical Shift = 59

(c) Period = 24

[tex]\bold{(d)\quad y=19\cos\bigg(\dfrac{\pi}{12}x\bigg)+59}[/tex]

(e) The model = 50°, the actual value = 52°

Step-by-step explanation:

The equation of a cosine function is: y = A cos (Bx - C) + D where

(a) Amplitude (A) = (Max - Min)/2

= (77 - 40)/2

= 37/2

= 18.5 (I rounded it up to 19)

(b) Vertical Shift (aka Center) (D)= (Max + Min)/2

= (77 + 40)/2

= 117/2

= 58.5 (I rounded it up to 59)

(c) Period (P) = 24

B = 2π/P

= 2π/24

= π/12

(d) There is no Phase Shift because the max is on the y-axis.

A = 19, B = π/12, C = 0, D = 59

⇒ y = 19 cos(π/12)x + 59

(e) let x = -2 (-2 represents 10 am on the graph)

⇒ y = 19 cos(π/12)(-2) + 59

= 19 cos (-π/6) + 59

= 19(-1/2) + 59

= -9.5 + 59

= 49.5

The model estimates the temperature at 10 am to be ≈ 50°

The actual temperature from the table is 52°