What is the constant of proportionality in this proportional relationship?
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The term "autonomous" refers to an ordinary differential equation that relates the derivatives of the dependent variable as a function *only* of the dependent variable. In other words, the ODE doesn't explicitly depend on the independent variable.
Examples:
is autonomous
is *not* autonomous
Examples:
Answer: After about 9.03 hours the temperature first reach 82 degrees.
Step-by-step explanation:
The sinusoidal function is given by :
where, A = amplitude; , α= phase shift on the Y-axis and C = midline.
As per given,
Average daily temperature= [midline is average of upper and lower limit.]
A= 97-85 = 12
Phase shift:
Period = 24 hours;
Substitute all values in sinusoidal function, we get
Put y= 82, we get
Hence, After about 9.03 hours the temperature first reach 82 degrees.