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?

  (a) Amplitude = 19

                 (b) Vertical Shift = 59

                 (c) Period = 24                

                 (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°

you can not drow on this

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752