The following function gives the temperature (in degrees Celsius) at the beach in Miami, Florida, t hours...

Question

The following function gives the temperature (in degrees Celsius) at the beach in Miami, Florida, t hours after midnight on a certain day:
M(t) = -6 * sin((π/12) * t) + 18
What is the instantaneous rate of change of the temperature at 9 a.m.?
Choose 1 answer:
A) 1.11 degrees Celsius per hour
B) 1.11 degrees Celsius
C) 13.76 degrees Celsius per hour
D) 13.76 degrees Celsius

SnapAndSolve AI · Accepted Answer

To find the instantaneous rate of change of the temperature at 9 a.m., we need to find the derivative of M(t) and evaluate it at t = 9.

The derivative of M(t) with respect to t is:

M'(t) = -6 * cos((π/12) * t) * (π/12)

Evaluating M'(t) at t = 9:

M'(9) = -6 * cos((π/12) * 9) * (π/12)

Calculating the value:

M'(9) = -6 * cos((3π/4)) * (π/12)

cos(3π/4) = -√2/2

M'(9) = -6 * (-√2/2) * (π/12)

M'(9) = (6√2π)/24

M'(9) = (√2π)/4

Approximating the value gives approximately 1.11 degrees Celsius per hour.

The correct answer is A) 1.11 degrees Celsius per hour.

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The following function gives the temperature (in degrees Celsius) at the beach in Miami, Florida, t hours...

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