Answer:
The sinusoidal wave can be represented by the equation:y=A∗sin[ω(x−α)]+Cy=A∗sin[ω(x−α)]+C
where, A is the amplitude; ω=2π/periodω=2π/period; α=α= phase shift on the Y-axis; and C = midline.
With the information given in this problem,
Midline (C) is the average calculated as: (72+38)/2=55(72+38)/2=55;
Amplitude (A) is 72-55= 17;
Period = 24 hours;
ω=2π/24ω=2π/24;
α=10α=10;
Substituting in the equation,
y=17∗sin[2π/24(x−10)]+55y=17∗sin[2π/24(x−10)]+55
Solving this equation for y=51y=51 gives the value of x as 9.09.
Thus, the temperature first reaches 51 degrees about 9.09 hours after midnight.
Step-by-step explanation:
