The temperature, t, in degrees celsius, in a warehouse changes according to the function t(h) = 18 + 4sin(pi/12 (x = 8)).
2 answers:
Answer:
about 1.01 °C per hour
Step-by-step explanation:
We assume the intended temperature function is ...
t(h) = 18 +4·sin(π/12(h -8))
We are asked for the rate of change when h=9.
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<h3>derivative</h3>The rate of change of temperature with respect to time is the derivative of t(h) with respect to h.
t'(h) = 4(π/12)cos(π/12(h -8)) = π/3·cos(π/12(h -8))
<h3>at 9 am</h3>For h = 9 hours after midnight, the rate of change is ...
t'(9) = π/3·cos(π/12(9 -8)) = π/3·cos(π/12) ≈ (3.14159)(0.965926)/3
t'(9) ≈ 1.01152
The rate of change of temperature at 9 a.m. is about 1.01 °C/hour.
The rate at which the temperature is changing at 9 a.m. is 19.03 degrees Celsius per hour
<h3>How to determine the rate at 9a.m?</h3>The function is given as:
9a.m is 9 hours since midnight.
This means that
x = 9
So, we have:
Evaluate
Evaluate the expression
t(h) = 19.03
Hence, the rate at which the temperature is changing at 9 a.m. is 19.03 degrees Celsius per hour
Read more about rates at:
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